1d:I[72985,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],"default"] 1e:I[63508,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],"default"] 1f:T1b24,

A single-loop series DC circuit consists of a constant DC voltage source ( $V_s$ ) of 12 V connected in series with a voltage-dropping resistor ( $R_1$ ) and a second resistive load ( $R_2$ ). When measured with a multimeter, the voltage drop across the first resistor ( $V_1$ ) is 4 V, and a continuous loop current ( $I$ ) of 2 A flows around the circuit. Using Kirchhoff's Voltage Law (KVL) and Ohm's Law, calculate the voltage drop across the second load ( $V_2$ ) and the electrical resistance of the second load ( $R_2$ ). (Note: You can modify the variables in the input data section)

20:Tde7,

Click to view KVL Loop Sign Convention Reference Table

When traversing the closed loop clockwise (following the direction of loop current I), the algebraic sign of each voltage term in the KVL equation (ΣV = 0) is assigned as follows:

Traversal Path Across Element	Potential Change	Term in ΣV = 0
Across DC source from negative (−) to positive (+) terminal	Voltage Rise	+V_s
Across resistor 1 with current from positive (+) to negative (−)	Voltage Drop	−V₁
Across load 2 with current from positive (+) to negative (−)	Voltage Drop	−V₂

21:T3a53,

Step 1: Calculate the voltage drop across the second load ( $V_2$ ) using Kirchhoff's Voltage Law (KVL) (From the closed-loop voltage balance equation $\sum V = +V_s - V_1 - V_2 = 0$ , rearrange to solve for the remaining voltage drop across the second load)

💡 Verification Tip: You can immediately verify the result by substituting $V_2$ back into the closed-loop equation $+V_s - V_1 - V_2 = 0$ . In any single-loop series circuit, the sum of all individual load voltage drops ( $V_1 + V_2$ ) must always equal the supply voltage ( $V_s$ ).

Step 2: Calculate the electrical resistance of the second load ( $R_2$ ) (Because all elements are connected in a single series loop, the same current $I$ flows through every component, allowing the load resistance $R_2$ to be determined via Ohm's Law)

22:T1615,

From the first step calculation using Kirchhoff's Voltage Law (KVL), when the DC supply provides and is dropped across the first series resistor, the remaining must appear across the second load so that the net potential change around the closed loop is zero. In engineering practice, this principle allows resistor $R_1$ (which has a resistance of ) to act as a series voltage-dropping resistor, stepping down a higher supply voltage to match the operating voltage rating of a downstream load.

In the second step, with a loop current of , the second load requires an equivalent resistance of and absorbs of electrical power (from $P_2 = V_2 \times I$ ), while the dropping resistor $R_1$ dissipates as heat, matching the total power of delivered by the source. Engineers use these linked voltage, resistance, and power values to select resistors with an adequate power rating (typically 1.5 to 2 times the calculated dissipation) so components do not overheat during continuous operation.

12:["$","main",null,{"className":"max-w-6xl mx-auto py-12 px-6","children":[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Article\",\"headline\":\"Calculation Example: Kirchhoff's Voltage Law (Single-Loop Circuit)\",\"description\":\"Worked calculation example for analyzing voltage drops and load resistance in a closed single-loop DC circuit using Kirchhoff's Voltage Law (KVL).\",\"keywords\":\"\",\"url\":\"https://wisawakorn.com/en/knowledge/calculations/kvl-single-loop-example\",\"mainEntityOfPage\":{\"@type\":\"WebPage\",\"@id\":\"https://wisawakorn.com/en/knowledge/calculations/kvl-single-loop-example\"},\"inLanguage\":\"en-US\"}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://wisawakorn.com/en\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Knowledge\",\"item\":\"https://wisawakorn.com/en/knowledge\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Calculations\",\"item\":\"https://wisawakorn.com/en/knowledge/calculations\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Calculation Example: Kirchhoff's Voltage Law (Single-Loop Circuit)\",\"item\":\"https://wisawakorn.com/en/knowledge/calculations/kvl-single-loop-example\"}]}"}}],["$","div",null,{"className":"grid grid-cols-1 lg:grid-cols-12 gap-12","children":[["$","div",null,{"className":"lg:col-span-8 xl:col-span-9","children":[["$","$L1d",null,{"text":"Back"}],["$","header",null,{"className":"mb-10","children":["$","h1",null,{"className":"text-4xl sm:text-5xl font-bold text-gray-900 dark:text-gray-100 tracking-tight mb-4","children":"Calculation Example: Kirchhoff's Voltage Law (Single-Loop Circuit)"}]}],["$","div",null,{"className":"prose prose-lg dark:prose-invert max-w-none","children":["$","$L1e",null,{"htmlContent":"

This example demonstrates how to apply Kirchhoff's Voltage Law (KVL) together with Ohm's Law to determine the unknown voltage drop in a single-loop series DC circuit and calculate the corresponding load resistance while maintaining closed-loop energy balance.

","components":[{"id":"__component_2__","type":"ExampleSection","props":{"title":"1. Problem Statement"},"children":"$1f"},{"id":"__component_3__","type":"IVPRenderer","props":{"id":"electrical-kvl-single-loop-engine"},"children":""},{"id":"__component_6__","type":"ExampleValue","props":{"type":"USER_INPUT","label":"DC source voltage (V_s)","value":"12","unit":"V","variableId":"V_s"},"children":""},{"id":"__component_7__","type":"ExampleValue","props":{"type":"USER_INPUT","label":"Voltage drop across resistor 1 (V₁)","value":"4","unit":"V","variableId":"V_1"},"children":""},{"id":"__component_8__","type":"ExampleValue","props":{"type":"USER_INPUT","label":"Loop current (I)","value":"2","unit":"A","variableId":"I"},"children":""},{"id":"__component_5__","type":"ExampleDataGroup","props":{},"children":"

"},{"id":"__component_4__","type":"ExampleSection","props":{"title":"2. Input Data"},"children":"$20"},{"id":"__component_10__","type":"ResultExplanation","props":{"formulaId":"kvl-single-loop-voltage","lang":"en","inputVariables":"{\"V_s\":{\"value\":12,\"unit\":\"V\"},\"V_1\":{\"value\":4,\"unit\":\"V\"}}","result":"{\"value\":8,\"unit\":\"V\"}","interactiveResult":"V_2","interactiveMap":"{\"V_s\":\"V_s\",\"V_1\":\"V_1\"}","substitutionTemplate":"V_2 = [V_s] - [V_1]"},"children":""},{"id":"__component_11__","type":"ResultExplanation","props":{"formulaId":"kvl-load-resistance","lang":"en","inputVariables":"{\"V_2\":{\"value\":8,\"unit\":\"V\"},\"I\":{\"value\":2,\"unit\":\"A\"}}","result":"{\"value\":4,\"unit\":\"Ω\"}","interactiveResult":"R_2","interactiveMap":"{\"V_2\":\"V_2\",\"I\":\"I\"}","substitutionTemplate":"R_2 = \\frac{[V_2]}{[I]}"},"children":""},{"id":"__component_9__","type":"ExampleSection","props":{"title":"3. Result Calculation"},"children":"$21"},{"id":"__component_13__","type":"DynamicText","props":{"variableId":"V_s","isResult":"false","fallback":"12","unit":"V"},"children":""},{"id":"__component_14__","type":"DynamicText","props":{"variableId":"V_1","isResult":"false","fallback":"4","unit":"V"},"children":""},{"id":"__component_15__","type":"DynamicText","props":{"variableId":"V_2","isResult":"true","fallback":"8","unit":"V"},"children":""},{"id":"__component_16__","type":"DynamicText","props":{"variableId":"R_1","isResult":"true","fallback":"2","unit":"Ω"},"children":""},{"id":"__component_17__","type":"DynamicText","props":{"variableId":"I","isResult":"false","fallback":"2","unit":"A"},"children":""},{"id":"__component_18__","type":"DynamicText","props":{"variableId":"R_2","isResult":"true","fallback":"4","unit":"Ω"},"children":""},{"id":"__component_19__","type":"DynamicText","props":{"variableId":"P_2","isResult":"true","fallback":"16","unit":"W"},"children":""},{"id":"__component_20__","type":"DynamicText","props":{"variableId":"P_1","isResult":"true","fallback":"8","unit":"W"},"children":""},{"id":"__component_21__","type":"DynamicText","props":{"variableId":"P_s","isResult":"true","fallback":"24","unit":"W"},"children":""},{"id":"__component_12__","type":"ExampleSection","props":{"title":"4. Engineering Significance"},"children":"$22"},{"id":"__component_1__","type":"WorkedExample","props":{"title":"Analyzing Voltage Drop and Load Resistance in a Single-Loop Series Circuit","id":"example-1"},"children":"

"},{"id":"__component_0__","type":"InteractiveVisualization","props":{"id":"electrical-kvl-single-loop-engine","version":"1.0.0","initialValues":"{\"V_s\":12,\"V_1\":4,\"I\":2}","hideControls":"true","hideRenderer":"true"},"children":"

"}]}]}],"$L23"]}],"$L24"]}]]}] 25:I[22016,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],""] 26:I[58681,["/_next/static/chunks/3th5o5azza5j1.js","/_next/static/chunks/0953gtd9gbswy.js","/_next/static/chunks/01oly6y_17ki0.js","/_next/static/chunks/1xlwfijmtjgqj.js","/_next/static/chunks/2hzca_9a7jrui.js","/_next/static/chunks/0_v6xzhg0htsf.js","/_next/static/chunks/2x0yuymt3nfdv.js","/_next/static/chunks/1hjnhv8wc11is.js"],"default"] 23:["$","section",null,{"aria-label":"Related Content","className":"mt-16 pt-8 border-t border-gray-200 dark:border-gray-800","children":[["$","h2",null,{"className":"text-2xl font-bold mb-6 text-gray-900 dark:text-gray-100","children":"Related Content"}],["$","div",null,{"className":"mb-8","children":[["$","h3",null,{"className":"text-lg font-semibold mb-4 text-gray-700 dark:text-gray-300","children":"Articles"}],["$","div",null,{"className":"grid grid-cols-1 md:grid-cols-2 gap-4","children":[["$","$L25","kirchhoffs-laws",{"href":"/en/knowledge/fundamentals/kirchhoffs-laws","className":"block p-4 bg-gray-50 dark:bg-[#111] rounded-xl border border-gray-200 dark:border-gray-800 hover:border-red-500 dark:hover:border-red-500 transition-colors focus:outline-none focus:ring-2 focus:ring-red-500","children":[["$","h4",null,{"className":"font-bold text-gray-900 dark:text-gray-100 mb-1","children":"Kirchhoff's Laws"}],["$","p",null,{"className":"text-sm text-gray-600 dark:text-gray-400 line-clamp-2","children":"Apply conservation of charge and energy to electrical nodes and loops using Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL)."}]]}]]}]]}],false]}] 24:["$","aside",null,{"className":"lg:col-span-4 xl:col-span-3 space-y-8","children":["$","div",null,{"className":"sticky top-8","children":["$","$L26",null,{}]}]}]