Simulador Leyes de Kirchhoff<\/title>\r\n<style>\r\n*{box-sizing:border-box;margin:0;padding:0}\r\nbody{font-family:system-ui,sans-serif;background:#f5f5f2;color:#1a1a1a;padding:16px}\r\n.sr-only{position:absolute;width:1px;height:1px;overflow:hidden;clip:rect(0,0,0,0)}\r\n.layout{display:grid;grid-template-columns:1fr 290px;gap:14px;padding:12px 0}\r\n.svgwrap{background:#fff;border:1px solid #ddd;border-radius:12px;overflow:hidden}\r\nsvg{display:block;width:100%}\r\n.sec-title{font-size:11px;font-weight:500;color:#666;text-transform:uppercase;letter-spacing:.06em;margin:12px 0 6px}\r\n.branch-card{background:#f1efe8;border-radius:8px;padding:8px 10px;margin-bottom:8px}\r\n.branch-title{font-size:12px;font-weight:500;color:#1a1a1a;margin-bottom:6px;display:flex;align-items:center;gap:6px}\r\n.dot{width:9px;height:9px;border-radius:50%;display:inline-block;flex-shrink:0}\r\n.row{display:flex;align-items:center;gap:6px;margin-bottom:4px}\r\n.row label{font-size:11px;color:#555;width:26px;flex-shrink:0}\r\n.row input[type=range]{flex:1;accent-color:#185FA5}\r\n.row .rv{font-size:11px;font-weight:500;color:#1a1a1a;min-width:36px;text-align:right}\r\n.btn-row{display:flex;gap:5px;margin-top:5px;flex-wrap:wrap}\r\n.tbtn{font-size:10px;padding:2px 7px;border:1px solid #bbb;border-radius:6px;background:#fff;color:#555;cursor:pointer;transition:background .15s}\r\n.tbtn.on{background:#185FA5;color:#fff;border-color:#185FA5}\r\n.tbtn.on2{background:#3B6D11;color:#fff;border-color:#3B6D11}\r\n.results-grid{display:grid;grid-template-columns:1fr 1fr;gap:6px;margin-bottom:10px}\r\n.mcard{background:#f1efe8;border-radius:8px;padding:7px 9px}\r\n.mcard .ml{font-size:10px;color:#666}\r\n.mcard .mv{font-size:15px;font-weight:500;color:#1a1a1a}\r\n.mcard .mu{font-size:10px;color:#666}\r\n.ptable{width:100%;border-collapse:collapse;font-size:11px}\r\n.ptable th{font-weight:500;padding:3px 5px;border-bottom:1px solid #ddd;color:#666;text-align:left}\r\n.ptable td{padding:3px 5px;border-bottom:1px solid #eee;color:#1a1a1a}\r\n.pos{color:#185FA5}.neg{color:#A32D2D}\r\n.warn{background:#faeeda;color:#633806;border-radius:8px;padding:5px 9px;font-size:11px;margin-bottom:8px;display:none}\r\n.eqbox{background:#f1efe8;border-radius:8px;padding:8px 10px;font-size:11px;font-family:monospace;line-height:1.8;margin-bottom:8px;color:#1a1a1a;white-space:pre}\r\nh1{font-size:18px;font-weight:500;margin-bottom:4px;color:#1a1a1a}\r\n.subtitle{font-size:12px;color:#666;margin-bottom:12px}\r\n<\/style>\r\n<\/head>\r\n<body>\r\n\r\n<h1>Simulador \u2014 Leyes de Kirchhoff<\/h1>\r\n<p class=\"subtitle\">Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos.<\/p>\r\n\r\n<div class=\"layout\">\r\n<div>\r\n <div class=\"svgwrap\">\r\n <svg id=\"circ\" viewBox=\"0 0 420 340\"><\/svg>\r\n <\/div>\r\n <div id=\"warnbox\" class=\"warn\">Sistema sin soluci\u00f3n \u2014 revis\u00e1 los valores.<\/div>\r\n <div style=\"margin-top:10px\">\r\n <div class=\"sec-title\">Resultados por rama<\/div>\r\n <table class=\"ptable\" id=\"restable\">\r\n <thead><tr><th>Rama<\/th><th>\u03b5 (V)<\/th><th>R (\u03a9)<\/th><th>I (A)<\/th><th>V_R (V)<\/th><th>P_fuente (W)<\/th><th>P_res (W)<\/th><\/tr><\/thead>\r\n <tbody id=\"restbody\"><\/tbody>\r\n <\/table>\r\n <\/div>\r\n <div style=\"margin-top:10px\">\r\n <div class=\"sec-title\">Ecuaciones (m\u00e9todo de nodos \u2014 KCL)<\/div>\r\n <div class=\"eqbox\" id=\"eqbox\"><\/div>\r\n <\/div>\r\n<\/div>\r\n\r\n<div>\r\n <div class=\"results-grid\" id=\"sumcards\"><\/div>\r\n <div id=\"branchcontrols\"><\/div>\r\n<\/div>\r\n<\/div>\r\n\r\n<script>\r\nconst BRANCH_COLORS = ['#185FA5','#3B6D11','#993C1D'];\r\nconst BRANCH_NAMES = ['Rama 1 (izq)','Rama 2 (centro)','Rama 3 (der)'];\r\n\r\nconst state = {\r\n branches: [\r\n {e:12, r:5, eDir:1, iDir:1, showI:false, showPol:false},\r\n {e:6, r:4, eDir:1, iDir:1, showI:false, showPol:false},\r\n {e:6, r:6, eDir:1, iDir:1, showI:false, showPol:false},\r\n ]\r\n};\r\n\r\nfunction buildControls(){\r\n const wrap = document.getElementById('branchcontrols');\r\n wrap.innerHTML = '';\r\n state.branches.forEach((b,i)=>{\r\n const col = BRANCH_COLORS[i];\r\n const card = document.createElement('div');\r\n card.className = 'branch-card';\r\n card.id = 'bc'+i;\r\n card.innerHTML = `\r\n <div class=\"branch-title\"><span class=\"dot\" style=\"background:${col}\"><\/span>${BRANCH_NAMES[i]}<\/div>\r\n <div class=\"row\"><label>\u03b5<\/label><input type=\"range\" id=\"e${i}\" min=\"0\" max=\"20\" step=\"0.5\" value=\"${b.e}\"><span class=\"rv\" id=\"ev${i}\">${b.e.toFixed(1)} V<\/span><\/div>\r\n <div class=\"row\"><label>R<\/label><input type=\"range\" id=\"r${i}\" min=\"1\" max=\"50\" step=\"1\" value=\"${b.r}\"><span class=\"rv\" id=\"rv${i}\">${b.r} \u03a9<\/span><\/div>\r\n <div class=\"btn-row\">\r\n <button class=\"tbtn ${b.eDir===1?'on':''}\" id=\"ed${i}\">\u03b5: + arriba<\/button>\r\n <button class=\"tbtn ${b.iDir===1?'on':''}\" id=\"id${i}\">I: sube<\/button>\r\n <button class=\"tbtn ${b.showI?'on2':''}\" id=\"si${i}\">Mostrar I<\/button>\r\n <button class=\"tbtn ${b.showPol?'on2':''}\" id=\"sp${i}\">+ y \u2212<\/button>\r\n <\/div>\r\n `;\r\n wrap.appendChild(card);\r\n\r\n document.getElementById('e'+i).addEventListener('input', ev=>{\r\n state.branches[i].e = +ev.target.value;\r\n document.getElementById('ev'+i).textContent = (+ev.target.value).toFixed(1)+' V';\r\n update();\r\n });\r\n document.getElementById('r'+i).addEventListener('input', ev=>{\r\n state.branches[i].r = +ev.target.value;\r\n document.getElementById('rv'+i).textContent = (+ev.target.value)+' \u03a9';\r\n update();\r\n });\r\n document.getElementById('ed'+i).addEventListener('click', ()=>{\r\n state.branches[i].eDir *= -1;\r\n const btn = document.getElementById('ed'+i);\r\n btn.textContent = state.branches[i].eDir===1 ? '\u03b5: + arriba' : '\u03b5: + abajo';\r\n btn.className = 'tbtn'+(state.branches[i].eDir===1?' on':'');\r\n update();\r\n });\r\n document.getElementById('id'+i).addEventListener('click', ()=>{\r\n state.branches[i].iDir *= -1;\r\n const btn = document.getElementById('id'+i);\r\n btn.textContent = state.branches[i].iDir===1 ? 'I: sube' : 'I: baja';\r\n btn.className = 'tbtn'+(state.branches[i].iDir===1?' on':'');\r\n update();\r\n });\r\n document.getElementById('si'+i).addEventListener('click', ()=>{\r\n state.branches[i].showI = !state.branches[i].showI;\r\n document.getElementById('si'+i).className = 'tbtn'+(state.branches[i].showI?' on2':'');\r\n update();\r\n });\r\n document.getElementById('sp'+i).addEventListener('click', ()=>{\r\n state.branches[i].showPol = !state.branches[i].showPol;\r\n document.getElementById('sp'+i).className = 'tbtn'+(state.branches[i].showPol?' on2':'');\r\n update();\r\n });\r\n });\r\n}\r\n\r\nconst NS = 'http:\/\/www.w3.org\/2000\/svg';\r\nfunction svgEl(tag,attrs,txt){\r\n const e = document.createElementNS(NS,tag);\r\n Object.entries(attrs).forEach(([k,v])=>e.setAttribute(k,v));\r\n if(txt!==undefined) e.textContent = txt;\r\n return e;\r\n}\r\n\r\nfunction zigzag(svg,x,y,len,horiz,col){\r\n const n=5, amp=6;\r\n let pts='';\r\n if(horiz){\r\n pts=`${x},${y}`;\r\n for(let i=0;i<n;i++){\r\n const t1=(i+.25)\/n, t2=(i+.75)\/n;\r\n pts+=` ${x+t1*len},${y+(i%2?amp:-amp)} ${x+t2*len},${y+(i%2?-amp:amp)}`;\r\n }\r\n pts+=` ${x+len},${y}`;\r\n } else {\r\n pts=`${x},${y}`;\r\n for(let i=0;i<n;i++){\r\n const t1=(i+.25)\/n, t2=(i+.75)\/n;\r\n pts+=` ${x+(i%2?amp:-amp)},${y+t1*len} ${x+(i%2?-amp:amp)},${y+t2*len}`;\r\n }\r\n pts+=` ${x},${y+len}`;\r\n }\r\n svg.appendChild(svgEl('polyline',{points:pts,fill:'none',stroke:col,strokeWidth:'2',strokeLinecap:'round'}));\r\n}\r\n\r\nfunction battery(svg,cx,cy,isVert,plusAtTop,col,eVal,showPol){\r\n if(isVert){\r\n const y1=cy-16, y2=cy+16;\r\n svg.appendChild(svgEl('line',{x1:cx,y1,x2:cx,y2:cy-3,stroke:col,strokeWidth:'1.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx,y1:cy+3,x2:cx,y2,stroke:col,strokeWidth:'1.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx-8,y1:cy-3,x2:cx+8,y2:cy-3,stroke:col,strokeWidth:'2.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx-5,y1:cy+3,x2:cx+5,y2:cy+3,stroke:col,strokeWidth:'1.5'}));\r\n const topSign = plusAtTop?'+':'\u2212';\r\n const botSign = plusAtTop?'\u2212':'+';\r\n svg.appendChild(svgEl('text',{x:cx+11,y:cy-8,'font-size':'10',fill:col,'font-weight':'500'},topSign));\r\n svg.appendChild(svgEl('text',{x:cx+11,y:cy+12,'font-size':'10',fill:col,'font-weight':'500'},botSign));\r\n svg.appendChild(svgEl('text',{x:cx-20,y:cy+4,'font-size':'10',fill:col,'text-anchor':'middle'},eVal.toFixed(1)+'V'));\r\n if(showPol){\r\n const psign=plusAtTop?'+':'\u2212';\r\n const nsign=plusAtTop?'\u2212':'+';\r\n svg.appendChild(svgEl('circle',{cx:cx+1,cy:cy-22,r:'6',fill:'none',stroke:'#E24B4A',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx+1,y:cy-18,'font-size':'9',fill:'#E24B4A','text-anchor':'middle','font-weight':'500'},psign));\r\n svg.appendChild(svgEl('circle',{cx:cx+1,cy:cy+22,r:'6',fill:'none',stroke:'#E24B4A',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx+1,y:cy+26,'font-size':'9',fill:'#E24B4A','text-anchor':'middle','font-weight':'500'},nsign));\r\n }\r\n }\r\n}\r\n\r\nfunction resistorLabel(svg,cx,cy,rVal,showPol,vDrop,col){\r\n svg.appendChild(svgEl('text',{x:cx+14,y:cy+3,'font-size':'10',fill:col},rVal+'\u03a9'));\r\n if(showPol){\r\n const pSign = vDrop>=0 ? '+' : '\u2212';\r\n const nSign = vDrop>=0 ? '\u2212' : '+';\r\n svg.appendChild(svgEl('circle',{cx:cx-2,cy:cy-18,r:'6',fill:'none',stroke:'#A32D2D',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx-2,y:cy-14,'font-size':'9',fill:'#A32D2D','text-anchor':'middle','font-weight':'500'},pSign));\r\n svg.appendChild(svgEl('circle',{cx:cx-2,cy:cy+18,r:'6',fill:'none',stroke:'#A32D2D',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx-2,y:cy+22,'font-size':'9',fill:'#A32D2D','text-anchor':'middle','font-weight':'500'},nSign));\r\n }\r\n}\r\n\r\nfunction arrowHead(svg,x,y,up,col){\r\n const d = up?-1:1;\r\n const pts = `${x},${y} ${x-5},${y+d*9} ${x+5},${y+d*9}`;\r\n svg.appendChild(svgEl('polygon',{points:pts,fill:col}));\r\n}\r\n\r\nfunction solve(){\r\n const b = state.branches;\r\n const E = b.map(br=>br.e*br.eDir);\r\n const R = b.map(br=>br.r);\r\n const denom = R[0]*R[1] + R[0]*R[2] + R[1]*R[2];\r\n if(Math.abs(denom)<1e-12) return null;\r\n const Vab = (E[0]*R[1]*R[2] + E[1]*R[0]*R[2] + E[2]*R[0]*R[1]) \/ denom;\r\n const I = b.map((br,i)=>(E[i]-Vab)\/R[i]);\r\n return {I, Vab};\r\n}\r\n\r\nfunction drawCircuit(sol){\r\n const svg = document.getElementById('circ');\r\n while(svg.firstChild) svg.removeChild(svg.firstChild);\r\n\r\n const xL=60, xC=210, xR=360;\r\n const yT=40, yB=300;\r\n const ymid=(yT+yB)\/2;\r\n const wire='#888';\r\n\r\n svg.appendChild(svgEl('line',{x1:xL,y1:yT,x2:xR,y2:yT,stroke:wire,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:xL,y1:yB,x2:xR,y2:yB,stroke:wire,strokeWidth:'2'}));\r\n\r\n [[xL,yT,'A'],[xC,yT,'B'],[xR,yT,'C'],\r\n [xL,yB,'D'],[xC,yB,'E'],[xR,yB,'F']].forEach(([x,y,lbl])=>{\r\n svg.appendChild(svgEl('circle',{cx:x,cy:y,r:'4',fill:wire}));\r\n const off = (lbl==='A'||lbl==='D')?-14:8;\r\n svg.appendChild(svgEl('text',{x:x+off,y:y+4,'font-size':'11',fill:'#666'},lbl));\r\n });\r\n\r\n const xs=[xL,xC,xR];\r\n state.branches.forEach((b,i)=>{\r\n const x = xs[i];\r\n const col = BRANCH_COLORS[i];\r\n const Ival = sol ? sol.I[i] : null;\r\n const vDrop = Ival!==null ? Ival*b.r : 0;\r\n\r\n svg.appendChild(svgEl('line',{x1:x,y1:yT,x2:x,y2:ymid-60,stroke:col,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:x,y1:ymid-30,x2:x,y2:ymid+10,stroke:col,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:x,y1:ymid+50,x2:x,y2:yB,stroke:col,strokeWidth:'2'}));\r\n\r\n zigzag(svg,x,ymid-60,30,false,col);\r\n resistorLabel(svg,x,ymid-45,b.r,b.showPol,vDrop,col);\r\n battery(svg,x,ymid+30,true,b.eDir===1,col,b.e,b.showPol);\r\n\r\n if(b.showI && Ival!==null){\r\n const up = (b.iDir===1 && Ival>0)||(b.iDir===-1 && Ival<0);\r\n const arY = ymid-5;\r\n arrowHead(svg,x,up?arY-4:arY+4,up,col);\r\n svg.appendChild(svgEl('text',{x:x-20,y:arY,'font-size':'10',fill:col,'text-anchor':'middle'},Math.abs(Ival).toFixed(3)+'A'));\r\n }\r\n });\r\n\r\n if(sol){\r\n svg.appendChild(svgEl('text',{x:210,y:22,'font-size':'10','text-anchor':'middle',fill:'#666'},\r\n 'Nodo superior V = '+sol.Vab.toFixed(3)+' V (ref: nodo inferior = 0 V)'));\r\n }\r\n}\r\n\r\nfunction updateResults(sol){\r\n const tbody = document.getElementById('restbody');\r\n tbody.innerHTML = '';\r\n const sumcards = document.getElementById('sumcards');\r\n const eqbox = document.getElementById('eqbox');\r\n\r\n if(!sol){\r\n document.getElementById('warnbox').style.display='block';\r\n sumcards.innerHTML='';\r\n eqbox.textContent='Sin soluci\u00f3n.';\r\n return;\r\n }\r\n document.getElementById('warnbox').style.display='none';\r\n\r\n let totalPdel=0, totalPabs=0, totalPdis=0;\r\n state.branches.forEach((b,i)=>{\r\n const I = sol.I[i];\r\n const VR = I*b.r;\r\n const Psrc = b.e*b.eDir*I;\r\n const Pres = I*I*b.r;\r\n if(Psrc>0) totalPdel+=Psrc; else totalPabs+=Math.abs(Psrc);\r\n totalPdis += Pres;\r\n\r\n const tr=document.createElement('tr');\r\n const col=BRANCH_COLORS[i];\r\n tr.innerHTML=`\r\n <td style=\"color:${col};font-weight:500\">${i+1}<\/td>\r\n <td>${(b.e*b.eDir).toFixed(1)}<\/td>\r\n <td>${b.r}<\/td>\r\n <td class=\"${I>=0?'pos':'neg'}\">${I.toFixed(4)}<\/td>\r\n <td>${VR.toFixed(3)}<\/td>\r\n <td class=\"${Psrc>=0?'pos':'neg'}\">${Psrc.toFixed(3)}<\/td>\r\n <td>${Pres.toFixed(3)}<\/td>\r\n `;\r\n tbody.appendChild(tr);\r\n });\r\n\r\n const kcl = sol.I.reduce((a,b)=>a+b,0);\r\n sumcards.innerHTML=`\r\n <div class=\"mcard\"><div class=\"ml\">V nodo superior<\/div><div class=\"mv\">${sol.Vab.toFixed(3)}<\/div><div class=\"mu\">V<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">KCL \u2014 \u03a3 I<\/div><div class=\"mv\">${kcl.toFixed(5)}<\/div><div class=\"mu\">A (\u22480)<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">P entregada<\/div><div class=\"mv\">${totalPdel.toFixed(3)}<\/div><div class=\"mu\">W<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">P disipada (R)<\/div><div class=\"mv\">${totalPdis.toFixed(3)}<\/div><div class=\"mu\">W<\/div><\/div>\r\n `;\r\n\r\n const b=state.branches;\r\n eqbox.textContent =\r\n 'KCL nodo superior: I\u2081 + I\u2082 + I\u2083 = 0\\n' +\r\n `Rama 1: I\u2081 = (\u03b5\u2081 \u2212 V) \/ R\u2081 = (${(b[0].e*b[0].eDir).toFixed(1)} \u2212 V) \/ ${b[0].r}\\n`+\r\n `Rama 2: I\u2082 = (\u03b5\u2082 \u2212 V) \/ R\u2082 = (${(b[1].e*b[1].eDir).toFixed(1)} \u2212 V) \/ ${b[1].r}\\n`+\r\n `Rama 3: I\u2083 = (\u03b5\u2083 \u2212 V) \/ R\u2083 = (${(b[2].e*b[2].eDir).toFixed(1)} \u2212 V) \/ ${b[2].r}\\n`+\r\n `\u2192 V_nodo = ${sol.Vab.toFixed(4)} V\\n`+\r\n `\u2192 I\u2081 = ${sol.I[0].toFixed(4)} A I\u2082 = ${sol.I[1].toFixed(4)} A I\u2083 = ${sol.I[2].toFixed(4)} A`;\r\n}\r\n\r\nfunction update(){\r\n const sol = solve();\r\n drawCircuit(sol);\r\n updateResults(sol);\r\n}\r\n\r\nbuildControls();\r\nupdate();\r\n<\/script>\r\n<\/body>\r\n<\/html>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Simulador Leyes de Kirchhoff Simulador \u2014 Leyes de Kirchhoff Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos. Sistema sin…<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-7184","page","type-page","status-publish","hentry"],"yoast_head":"\n<title>leyes_de_kirchhoff_1 - F\u00edsica 2<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fisica2.fica.unsl.edu.ar\/index.php\/leyes_de_kirchhoff_1\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"leyes_de_kirchhoff_1 - F\u00edsica 2\" \/>\n<meta property=\"og:description\" content=\"Simulador Leyes de Kirchhoff Simulador \u2014 Leyes de Kirchhoff Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos. 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\n\t\t\t\t\t\r\n\r\n\r\n\r\n\r\nSimulador Leyes de Kirchhoff<\/title>\r\n<style>\r\n*{box-sizing:border-box;margin:0;padding:0}\r\nbody{font-family:system-ui,sans-serif;background:#f5f5f2;color:#1a1a1a;padding:16px}\r\n.sr-only{position:absolute;width:1px;height:1px;overflow:hidden;clip:rect(0,0,0,0)}\r\n.layout{display:grid;grid-template-columns:1fr 290px;gap:14px;padding:12px 0}\r\n.svgwrap{background:#fff;border:1px solid #ddd;border-radius:12px;overflow:hidden}\r\nsvg{display:block;width:100%}\r\n.sec-title{font-size:11px;font-weight:500;color:#666;text-transform:uppercase;letter-spacing:.06em;margin:12px 0 6px}\r\n.branch-card{background:#f1efe8;border-radius:8px;padding:8px 10px;margin-bottom:8px}\r\n.branch-title{font-size:12px;font-weight:500;color:#1a1a1a;margin-bottom:6px;display:flex;align-items:center;gap:6px}\r\n.dot{width:9px;height:9px;border-radius:50%;display:inline-block;flex-shrink:0}\r\n.row{display:flex;align-items:center;gap:6px;margin-bottom:4px}\r\n.row label{font-size:11px;color:#555;width:26px;flex-shrink:0}\r\n.row input[type=range]{flex:1;accent-color:#185FA5}\r\n.row .rv{font-size:11px;font-weight:500;color:#1a1a1a;min-width:36px;text-align:right}\r\n.btn-row{display:flex;gap:5px;margin-top:5px;flex-wrap:wrap}\r\n.tbtn{font-size:10px;padding:2px 7px;border:1px solid #bbb;border-radius:6px;background:#fff;color:#555;cursor:pointer;transition:background .15s}\r\n.tbtn.on{background:#185FA5;color:#fff;border-color:#185FA5}\r\n.tbtn.on2{background:#3B6D11;color:#fff;border-color:#3B6D11}\r\n.results-grid{display:grid;grid-template-columns:1fr 1fr;gap:6px;margin-bottom:10px}\r\n.mcard{background:#f1efe8;border-radius:8px;padding:7px 9px}\r\n.mcard .ml{font-size:10px;color:#666}\r\n.mcard .mv{font-size:15px;font-weight:500;color:#1a1a1a}\r\n.mcard .mu{font-size:10px;color:#666}\r\n.ptable{width:100%;border-collapse:collapse;font-size:11px}\r\n.ptable th{font-weight:500;padding:3px 5px;border-bottom:1px solid #ddd;color:#666;text-align:left}\r\n.ptable td{padding:3px 5px;border-bottom:1px solid #eee;color:#1a1a1a}\r\n.pos{color:#185FA5}.neg{color:#A32D2D}\r\n.warn{background:#faeeda;color:#633806;border-radius:8px;padding:5px 9px;font-size:11px;margin-bottom:8px;display:none}\r\n.eqbox{background:#f1efe8;border-radius:8px;padding:8px 10px;font-size:11px;font-family:monospace;line-height:1.8;margin-bottom:8px;color:#1a1a1a;white-space:pre}\r\nh1{font-size:18px;font-weight:500;margin-bottom:4px;color:#1a1a1a}\r\n.subtitle{font-size:12px;color:#666;margin-bottom:12px}\r\n<\/style>\r\n<\/head>\r\n<body>\r\n\r\n<h1>Simulador \u2014 Leyes de Kirchhoff<\/h1>\r\n<p class=\"subtitle\">Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos.<\/p>\r\n\r\n<div class=\"layout\">\r\n<div>\r\n <div class=\"svgwrap\">\r\n <svg id=\"circ\" viewBox=\"0 0 420 340\"><\/svg>\r\n <\/div>\r\n <div id=\"warnbox\" class=\"warn\">Sistema sin soluci\u00f3n \u2014 revis\u00e1 los valores.<\/div>\r\n <div style=\"margin-top:10px\">\r\n <div class=\"sec-title\">Resultados por rama<\/div>\r\n <table class=\"ptable\" id=\"restable\">\r\n <thead><tr><th>Rama<\/th><th>\u03b5 (V)<\/th><th>R (\u03a9)<\/th><th>I (A)<\/th><th>V_R (V)<\/th><th>P_fuente (W)<\/th><th>P_res (W)<\/th><\/tr><\/thead>\r\n <tbody id=\"restbody\"><\/tbody>\r\n <\/table>\r\n <\/div>\r\n <div style=\"margin-top:10px\">\r\n <div class=\"sec-title\">Ecuaciones (m\u00e9todo de nodos \u2014 KCL)<\/div>\r\n <div class=\"eqbox\" id=\"eqbox\"><\/div>\r\n <\/div>\r\n<\/div>\r\n\r\n<div>\r\n <div class=\"results-grid\" id=\"sumcards\"><\/div>\r\n <div id=\"branchcontrols\"><\/div>\r\n<\/div>\r\n<\/div>\r\n\r\n<script>\r\nconst BRANCH_COLORS = ['#185FA5','#3B6D11','#993C1D'];\r\nconst BRANCH_NAMES = ['Rama 1 (izq)','Rama 2 (centro)','Rama 3 (der)'];\r\n\r\nconst state = {\r\n branches: [\r\n {e:12, r:5, eDir:1, iDir:1, showI:false, showPol:false},\r\n {e:6, r:4, eDir:1, iDir:1, showI:false, showPol:false},\r\n {e:6, r:6, eDir:1, iDir:1, showI:false, showPol:false},\r\n ]\r\n};\r\n\r\nfunction buildControls(){\r\n const wrap = document.getElementById('branchcontrols');\r\n wrap.innerHTML = '';\r\n state.branches.forEach((b,i)=>{\r\n const col = BRANCH_COLORS[i];\r\n const card = document.createElement('div');\r\n card.className = 'branch-card';\r\n card.id = 'bc'+i;\r\n card.innerHTML = `\r\n <div class=\"branch-title\"><span class=\"dot\" style=\"background:${col}\"><\/span>${BRANCH_NAMES[i]}<\/div>\r\n <div class=\"row\"><label>\u03b5<\/label><input type=\"range\" id=\"e${i}\" min=\"0\" max=\"20\" step=\"0.5\" value=\"${b.e}\"><span class=\"rv\" id=\"ev${i}\">${b.e.toFixed(1)} V<\/span><\/div>\r\n <div class=\"row\"><label>R<\/label><input type=\"range\" id=\"r${i}\" min=\"1\" max=\"50\" step=\"1\" value=\"${b.r}\"><span class=\"rv\" id=\"rv${i}\">${b.r} \u03a9<\/span><\/div>\r\n <div class=\"btn-row\">\r\n <button class=\"tbtn ${b.eDir===1?'on':''}\" id=\"ed${i}\">\u03b5: + arriba<\/button>\r\n <button class=\"tbtn ${b.iDir===1?'on':''}\" id=\"id${i}\">I: sube<\/button>\r\n <button class=\"tbtn ${b.showI?'on2':''}\" id=\"si${i}\">Mostrar I<\/button>\r\n <button class=\"tbtn ${b.showPol?'on2':''}\" id=\"sp${i}\">+ y \u2212<\/button>\r\n <\/div>\r\n `;\r\n wrap.appendChild(card);\r\n\r\n document.getElementById('e'+i).addEventListener('input', ev=>{\r\n state.branches[i].e = +ev.target.value;\r\n document.getElementById('ev'+i).textContent = (+ev.target.value).toFixed(1)+' V';\r\n update();\r\n });\r\n document.getElementById('r'+i).addEventListener('input', ev=>{\r\n state.branches[i].r = +ev.target.value;\r\n document.getElementById('rv'+i).textContent = (+ev.target.value)+' \u03a9';\r\n update();\r\n });\r\n document.getElementById('ed'+i).addEventListener('click', ()=>{\r\n state.branches[i].eDir *= -1;\r\n const btn = document.getElementById('ed'+i);\r\n btn.textContent = state.branches[i].eDir===1 ? '\u03b5: + arriba' : '\u03b5: + abajo';\r\n btn.className = 'tbtn'+(state.branches[i].eDir===1?' on':'');\r\n update();\r\n });\r\n document.getElementById('id'+i).addEventListener('click', ()=>{\r\n state.branches[i].iDir *= -1;\r\n const btn = document.getElementById('id'+i);\r\n btn.textContent = state.branches[i].iDir===1 ? 'I: sube' : 'I: baja';\r\n btn.className = 'tbtn'+(state.branches[i].iDir===1?' on':'');\r\n update();\r\n });\r\n document.getElementById('si'+i).addEventListener('click', ()=>{\r\n state.branches[i].showI = !state.branches[i].showI;\r\n document.getElementById('si'+i).className = 'tbtn'+(state.branches[i].showI?' on2':'');\r\n update();\r\n });\r\n document.getElementById('sp'+i).addEventListener('click', ()=>{\r\n state.branches[i].showPol = !state.branches[i].showPol;\r\n document.getElementById('sp'+i).className = 'tbtn'+(state.branches[i].showPol?' on2':'');\r\n update();\r\n });\r\n });\r\n}\r\n\r\nconst NS = 'http:\/\/www.w3.org\/2000\/svg';\r\nfunction svgEl(tag,attrs,txt){\r\n const e = document.createElementNS(NS,tag);\r\n Object.entries(attrs).forEach(([k,v])=>e.setAttribute(k,v));\r\n if(txt!==undefined) e.textContent = txt;\r\n return e;\r\n}\r\n\r\nfunction zigzag(svg,x,y,len,horiz,col){\r\n const n=5, amp=6;\r\n let pts='';\r\n if(horiz){\r\n pts=`${x},${y}`;\r\n for(let i=0;i<n;i++){\r\n const t1=(i+.25)\/n, t2=(i+.75)\/n;\r\n pts+=` ${x+t1*len},${y+(i%2?amp:-amp)} ${x+t2*len},${y+(i%2?-amp:amp)}`;\r\n }\r\n pts+=` ${x+len},${y}`;\r\n } else {\r\n pts=`${x},${y}`;\r\n for(let i=0;i<n;i++){\r\n const t1=(i+.25)\/n, t2=(i+.75)\/n;\r\n pts+=` ${x+(i%2?amp:-amp)},${y+t1*len} ${x+(i%2?-amp:amp)},${y+t2*len}`;\r\n }\r\n pts+=` ${x},${y+len}`;\r\n }\r\n svg.appendChild(svgEl('polyline',{points:pts,fill:'none',stroke:col,strokeWidth:'2',strokeLinecap:'round'}));\r\n}\r\n\r\nfunction battery(svg,cx,cy,isVert,plusAtTop,col,eVal,showPol){\r\n if(isVert){\r\n const y1=cy-16, y2=cy+16;\r\n svg.appendChild(svgEl('line',{x1:cx,y1,x2:cx,y2:cy-3,stroke:col,strokeWidth:'1.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx,y1:cy+3,x2:cx,y2,stroke:col,strokeWidth:'1.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx-8,y1:cy-3,x2:cx+8,y2:cy-3,stroke:col,strokeWidth:'2.5'}));\r\n svg.appendChild(svgEl('line',{x1:cx-5,y1:cy+3,x2:cx+5,y2:cy+3,stroke:col,strokeWidth:'1.5'}));\r\n const topSign = plusAtTop?'+':'\u2212';\r\n const botSign = plusAtTop?'\u2212':'+';\r\n svg.appendChild(svgEl('text',{x:cx+11,y:cy-8,'font-size':'10',fill:col,'font-weight':'500'},topSign));\r\n svg.appendChild(svgEl('text',{x:cx+11,y:cy+12,'font-size':'10',fill:col,'font-weight':'500'},botSign));\r\n svg.appendChild(svgEl('text',{x:cx-20,y:cy+4,'font-size':'10',fill:col,'text-anchor':'middle'},eVal.toFixed(1)+'V'));\r\n if(showPol){\r\n const psign=plusAtTop?'+':'\u2212';\r\n const nsign=plusAtTop?'\u2212':'+';\r\n svg.appendChild(svgEl('circle',{cx:cx+1,cy:cy-22,r:'6',fill:'none',stroke:'#E24B4A',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx+1,y:cy-18,'font-size':'9',fill:'#E24B4A','text-anchor':'middle','font-weight':'500'},psign));\r\n svg.appendChild(svgEl('circle',{cx:cx+1,cy:cy+22,r:'6',fill:'none',stroke:'#E24B4A',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx+1,y:cy+26,'font-size':'9',fill:'#E24B4A','text-anchor':'middle','font-weight':'500'},nsign));\r\n }\r\n }\r\n}\r\n\r\nfunction resistorLabel(svg,cx,cy,rVal,showPol,vDrop,col){\r\n svg.appendChild(svgEl('text',{x:cx+14,y:cy+3,'font-size':'10',fill:col},rVal+'\u03a9'));\r\n if(showPol){\r\n const pSign = vDrop>=0 ? '+' : '\u2212';\r\n const nSign = vDrop>=0 ? '\u2212' : '+';\r\n svg.appendChild(svgEl('circle',{cx:cx-2,cy:cy-18,r:'6',fill:'none',stroke:'#A32D2D',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx-2,y:cy-14,'font-size':'9',fill:'#A32D2D','text-anchor':'middle','font-weight':'500'},pSign));\r\n svg.appendChild(svgEl('circle',{cx:cx-2,cy:cy+18,r:'6',fill:'none',stroke:'#A32D2D',strokeWidth:'1'}));\r\n svg.appendChild(svgEl('text',{x:cx-2,y:cy+22,'font-size':'9',fill:'#A32D2D','text-anchor':'middle','font-weight':'500'},nSign));\r\n }\r\n}\r\n\r\nfunction arrowHead(svg,x,y,up,col){\r\n const d = up?-1:1;\r\n const pts = `${x},${y} ${x-5},${y+d*9} ${x+5},${y+d*9}`;\r\n svg.appendChild(svgEl('polygon',{points:pts,fill:col}));\r\n}\r\n\r\nfunction solve(){\r\n const b = state.branches;\r\n const E = b.map(br=>br.e*br.eDir);\r\n const R = b.map(br=>br.r);\r\n const denom = R[0]*R[1] + R[0]*R[2] + R[1]*R[2];\r\n if(Math.abs(denom)<1e-12) return null;\r\n const Vab = (E[0]*R[1]*R[2] + E[1]*R[0]*R[2] + E[2]*R[0]*R[1]) \/ denom;\r\n const I = b.map((br,i)=>(E[i]-Vab)\/R[i]);\r\n return {I, Vab};\r\n}\r\n\r\nfunction drawCircuit(sol){\r\n const svg = document.getElementById('circ');\r\n while(svg.firstChild) svg.removeChild(svg.firstChild);\r\n\r\n const xL=60, xC=210, xR=360;\r\n const yT=40, yB=300;\r\n const ymid=(yT+yB)\/2;\r\n const wire='#888';\r\n\r\n svg.appendChild(svgEl('line',{x1:xL,y1:yT,x2:xR,y2:yT,stroke:wire,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:xL,y1:yB,x2:xR,y2:yB,stroke:wire,strokeWidth:'2'}));\r\n\r\n [[xL,yT,'A'],[xC,yT,'B'],[xR,yT,'C'],\r\n [xL,yB,'D'],[xC,yB,'E'],[xR,yB,'F']].forEach(([x,y,lbl])=>{\r\n svg.appendChild(svgEl('circle',{cx:x,cy:y,r:'4',fill:wire}));\r\n const off = (lbl==='A'||lbl==='D')?-14:8;\r\n svg.appendChild(svgEl('text',{x:x+off,y:y+4,'font-size':'11',fill:'#666'},lbl));\r\n });\r\n\r\n const xs=[xL,xC,xR];\r\n state.branches.forEach((b,i)=>{\r\n const x = xs[i];\r\n const col = BRANCH_COLORS[i];\r\n const Ival = sol ? sol.I[i] : null;\r\n const vDrop = Ival!==null ? Ival*b.r : 0;\r\n\r\n svg.appendChild(svgEl('line',{x1:x,y1:yT,x2:x,y2:ymid-60,stroke:col,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:x,y1:ymid-30,x2:x,y2:ymid+10,stroke:col,strokeWidth:'2'}));\r\n svg.appendChild(svgEl('line',{x1:x,y1:ymid+50,x2:x,y2:yB,stroke:col,strokeWidth:'2'}));\r\n\r\n zigzag(svg,x,ymid-60,30,false,col);\r\n resistorLabel(svg,x,ymid-45,b.r,b.showPol,vDrop,col);\r\n battery(svg,x,ymid+30,true,b.eDir===1,col,b.e,b.showPol);\r\n\r\n if(b.showI && Ival!==null){\r\n const up = (b.iDir===1 && Ival>0)||(b.iDir===-1 && Ival<0);\r\n const arY = ymid-5;\r\n arrowHead(svg,x,up?arY-4:arY+4,up,col);\r\n svg.appendChild(svgEl('text',{x:x-20,y:arY,'font-size':'10',fill:col,'text-anchor':'middle'},Math.abs(Ival).toFixed(3)+'A'));\r\n }\r\n });\r\n\r\n if(sol){\r\n svg.appendChild(svgEl('text',{x:210,y:22,'font-size':'10','text-anchor':'middle',fill:'#666'},\r\n 'Nodo superior V = '+sol.Vab.toFixed(3)+' V (ref: nodo inferior = 0 V)'));\r\n }\r\n}\r\n\r\nfunction updateResults(sol){\r\n const tbody = document.getElementById('restbody');\r\n tbody.innerHTML = '';\r\n const sumcards = document.getElementById('sumcards');\r\n const eqbox = document.getElementById('eqbox');\r\n\r\n if(!sol){\r\n document.getElementById('warnbox').style.display='block';\r\n sumcards.innerHTML='';\r\n eqbox.textContent='Sin soluci\u00f3n.';\r\n return;\r\n }\r\n document.getElementById('warnbox').style.display='none';\r\n\r\n let totalPdel=0, totalPabs=0, totalPdis=0;\r\n state.branches.forEach((b,i)=>{\r\n const I = sol.I[i];\r\n const VR = I*b.r;\r\n const Psrc = b.e*b.eDir*I;\r\n const Pres = I*I*b.r;\r\n if(Psrc>0) totalPdel+=Psrc; else totalPabs+=Math.abs(Psrc);\r\n totalPdis += Pres;\r\n\r\n const tr=document.createElement('tr');\r\n const col=BRANCH_COLORS[i];\r\n tr.innerHTML=`\r\n <td style=\"color:${col};font-weight:500\">${i+1}<\/td>\r\n <td>${(b.e*b.eDir).toFixed(1)}<\/td>\r\n <td>${b.r}<\/td>\r\n <td class=\"${I>=0?'pos':'neg'}\">${I.toFixed(4)}<\/td>\r\n <td>${VR.toFixed(3)}<\/td>\r\n <td class=\"${Psrc>=0?'pos':'neg'}\">${Psrc.toFixed(3)}<\/td>\r\n <td>${Pres.toFixed(3)}<\/td>\r\n `;\r\n tbody.appendChild(tr);\r\n });\r\n\r\n const kcl = sol.I.reduce((a,b)=>a+b,0);\r\n sumcards.innerHTML=`\r\n <div class=\"mcard\"><div class=\"ml\">V nodo superior<\/div><div class=\"mv\">${sol.Vab.toFixed(3)}<\/div><div class=\"mu\">V<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">KCL \u2014 \u03a3 I<\/div><div class=\"mv\">${kcl.toFixed(5)}<\/div><div class=\"mu\">A (\u22480)<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">P entregada<\/div><div class=\"mv\">${totalPdel.toFixed(3)}<\/div><div class=\"mu\">W<\/div><\/div>\r\n <div class=\"mcard\"><div class=\"ml\">P disipada (R)<\/div><div class=\"mv\">${totalPdis.toFixed(3)}<\/div><div class=\"mu\">W<\/div><\/div>\r\n `;\r\n\r\n const b=state.branches;\r\n eqbox.textContent =\r\n 'KCL nodo superior: I\u2081 + I\u2082 + I\u2083 = 0\\n' +\r\n `Rama 1: I\u2081 = (\u03b5\u2081 \u2212 V) \/ R\u2081 = (${(b[0].e*b[0].eDir).toFixed(1)} \u2212 V) \/ ${b[0].r}\\n`+\r\n `Rama 2: I\u2082 = (\u03b5\u2082 \u2212 V) \/ R\u2082 = (${(b[1].e*b[1].eDir).toFixed(1)} \u2212 V) \/ ${b[1].r}\\n`+\r\n `Rama 3: I\u2083 = (\u03b5\u2083 \u2212 V) \/ R\u2083 = (${(b[2].e*b[2].eDir).toFixed(1)} \u2212 V) \/ ${b[2].r}\\n`+\r\n `\u2192 V_nodo = ${sol.Vab.toFixed(4)} V\\n`+\r\n `\u2192 I\u2081 = ${sol.I[0].toFixed(4)} A I\u2082 = ${sol.I[1].toFixed(4)} A I\u2083 = ${sol.I[2].toFixed(4)} A`;\r\n}\r\n\r\nfunction update(){\r\n const sol = solve();\r\n drawCircuit(sol);\r\n updateResults(sol);\r\n}\r\n\r\nbuildControls();\r\nupdate();\r\n<\/script>\r\n<\/body>\r\n<\/html>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Simulador Leyes de Kirchhoff Simulador \u2014 Leyes de Kirchhoff Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos. Sistema sin…<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-7184","page","type-page","status-publish","hentry"],"yoast_head":"\n<title>leyes_de_kirchhoff_1 - F\u00edsica 2<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fisica2.fica.unsl.edu.ar\/index.php\/leyes_de_kirchhoff_1\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"leyes_de_kirchhoff_1 - F\u00edsica 2\" \/>\n<meta property=\"og:description\" content=\"Simulador Leyes de Kirchhoff Simulador \u2014 Leyes de Kirchhoff Circuito de tres ramas paralelas con fuente y resistencia por rama. M\u00e9todo de nodos. 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M\u00e9todo de nodos. 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