Kirchhoff’s Law Calculator (KVL Series Circuit)

This Kirchhoff’s Law Calculator focuses on Kirchhoff’s Voltage Law (KVL) for a simple series circuit with up to three resistors and a single voltage source.

KVL Calculator: Series Circuit

Table of resistances, voltage drops, and power dissipation for each component in the series circuit.

Component	Resistance (Ω)	Voltage Drop (V)	Power (W)
R1	0	0	0
R2	0	0	0
R3	0	0	0
Total	0	0	0

What is Kirchhoff’s Law Calculator?

A Kirchhoff’s Law Calculator is a tool used to analyze electric circuits based on Gustav Kirchhoff’s circuit laws. There are two main laws: Kirchhoff’s Current Law (KCL) and Kirchhoff’s Voltage Law (KVL). This particular calculator focuses on KVL for a simple series circuit. KVL states that the sum of all voltage drops around any closed loop in a circuit must equal the sum of the electromotive forces (voltage sources) in that loop, or simply, the algebraic sum of voltages around a closed loop is zero.

Engineers, students, and hobbyists use a Kirchhoff’s Law Calculator to determine unknown currents, voltages, and resistances within a circuit without needing to physically measure them. Our KVL calculator helps you find the total current, individual voltage drops across resistors, and total resistance in a series circuit.

Who should use it?

• Electrical engineering students learning circuit analysis.
• Electronics hobbyists designing or troubleshooting circuits.
• Engineers and technicians working with electrical systems.

Common Misconceptions

• KVL applies to any path: KVL only applies to closed loops within a circuit.
• Ideal components: The calculator assumes ideal resistors and voltage sources (no internal resistance in the source, resistor values are exact). Real-world components have tolerances.
• This calculator solves all circuits: This specific Kirchhoff’s Law Calculator is for a simple series DC circuit. More complex circuits (parallel, series-parallel, AC) require more advanced analysis or different calculators like a node voltage analysis tool.

Kirchhoff’s Law Calculator Formula and Mathematical Explanation (KVL for Series Circuit)

For a simple series circuit with a voltage source (V_s) and resistors R₁, R₂, and R₃ connected in series, Kirchhoff’s Voltage Law (KVL) is applied.

KVL Equation: V_s – V₁ – V₂ – V₃ = 0, or V_s = V₁ + V₂ + V₃

Where V₁, V₂, and V₃ are the voltage drops across resistors R₁, R₂, and R₃ respectively.

Step-by-step Derivation:

1. Total Resistance (R_total): In a series circuit, the total resistance is the sum of individual resistances:
   Rtotal = R1 + R2 + R3
2. Total Current (I): Using Ohm’s Law, the total current (I) flowing through the series circuit is:
   I = Vs / Rtotal (This current is the same through all resistors in series).
3. Voltage Drops (V₁, V₂, V₃): Again, using Ohm’s Law for each resistor:
   V1 = I * R1
V2 = I * R2
V3 = I * R3
4. KVL Verification: Substituting the voltage drops back into the KVL equation:
   Vs = (I * R1) + (I * R2) + (I * R3) = I * (R1 + R2 + R3) = I * Rtotal
   Since I = Vs / Rtotal, then Vs = (Vs / Rtotal) * Rtotal = Vs, confirming KVL.

Variables Table

Variable	Meaning	Unit	Typical Range
Vs	Source Voltage	Volts (V)	0 – 1000+ V
R1, R2, R3	Resistances	Ohms (Ω)	0 – 1M+ Ω
Rtotal	Total Resistance	Ohms (Ω)	0 – 3M+ Ω
I	Total Current	Amperes (A) or mA	0 – 10+ A
V1, V2, V3	Voltage Drops across R1, R2, R3	Volts (V)	0 – Vs

Practical Examples (Real-World Use Cases)

Example 1: LED Circuit

You have a 9V battery (V_s=9V) and want to power an LED that requires about 2V and 20mA (0.02A). You use a current-limiting resistor (R1). Let’s say you chose a 330Ω resistor (R1=330Ω) and have another 100Ω resistor (R2=100Ω) in series just for this example (R3=0).

• V_s = 9V
• R₁ = 330Ω
• R₂ = 100Ω
• R₃ = 0Ω

Using the Kirchhoff’s Law Calculator (or the formulas):

• R_total = 330 + 100 + 0 = 430Ω
• I = 9V / 430Ω ≈ 0.0209 A (20.9 mA)
• V₁ = 0.0209A * 330Ω ≈ 6.90V
• V₂ = 0.0209A * 100Ω ≈ 2.09V
• KVL Check: 9V – 6.90V – 2.09V ≈ 0.01V (close to 0 due to rounding)

The voltage across R2 is around 2.09V, close to what an LED might drop. The current is around 20.9mA.

Example 2: Simple Voltage Divider

You have a 12V source (V_s=12V) and two resistors, R1=1000Ω and R2=2000Ω (R3=0), forming a voltage divider.

• V_s = 12V
• R₁ = 1000Ω
• R₂ = 2000Ω
• R₃ = 0Ω

Using the Kirchhoff’s Law Calculator:

• R_total = 1000 + 2000 = 3000Ω
• I = 12V / 3000Ω = 0.004 A (4 mA)
• V₁ = 0.004A * 1000Ω = 4V
• V₂ = 0.004A * 2000Ω = 8V
• KVL Check: 12V – 4V – 8V = 0V

The voltage across R2 is 8V. A voltage divider calculator would focus on this output.

How to Use This Kirchhoff’s Law Calculator

1. Enter Voltage Source (V_s): Input the voltage provided by your power source (e.g., battery, power supply) in Volts.
2. Enter Resistances (R₁, R₂, R₃): Input the values of the resistors in your series circuit in Ohms. If you have fewer than three resistors, enter 0 for the unused ones.
3. View Results: The calculator automatically updates the Total Current (I), Total Resistance (R_total), and individual Voltage Drops (V₁, V₂, V₃) as you type. The KVL check sum is also displayed.
4. Analyze Table and Chart: The table provides a breakdown of resistance, voltage drop, and power for each component. The chart visually represents the voltage drops.
5. Reset: Click “Reset” to return to default values.
6. Copy Results: Click “Copy Results” to copy the main outputs and inputs to your clipboard.

The primary result is the Total Current flowing through the series circuit. The intermediate results show how the voltage is distributed across the resistors. The KVL check should be very close to zero, confirming the calculations based on KVL.

Key Factors That Affect Kirchhoff’s Law Calculator Results

1. Source Voltage (V_s): A higher source voltage will result in a proportionally higher current (if resistance is constant) and larger voltage drops across each resistor.
2. Resistance Values (R₁, R₂, R₃): The total resistance directly affects the current (higher resistance, lower current for the same voltage). The individual resistance values determine how the total voltage is divided among them – larger resistances have larger voltage drops.
3. Number of Resistors: Adding more resistors in series increases the total resistance and decreases the current.
4. Component Tolerances: Real resistors have manufacturing tolerances (e.g., ±5%, ±1%). The actual resistance values can vary, leading to slight differences between calculated and measured values. Our Kirchhoff’s Law Calculator assumes ideal values. You can check resistor values using a resistor color code calculator.
5. Internal Resistance of Source: Real voltage sources have internal resistance, which can cause the terminal voltage to drop under load, slightly affecting the circuit current and voltage drops. The calculator assumes an ideal source (zero internal resistance).
6. Temperature: The resistance of most materials changes with temperature, which can affect the actual current and voltage drops in a real circuit, especially under high power conditions. The calculator does not account for temperature effects. More on power can be found with a power calculator.

Frequently Asked Questions (FAQ)

What is Kirchhoff’s Current Law (KCL)?

KCL states that the algebraic sum of currents entering and leaving a node (or junction) in an electrical circuit is zero. The sum of currents flowing into a node equals the sum of currents flowing out of that node. This Kirchhoff’s Law Calculator focuses on KVL.

What is Kirchhoff’s Voltage Law (KVL)?

KVL states that the algebraic sum of the voltages around any closed loop in a circuit is zero. The sum of voltage rises (from sources) equals the sum of voltage drops (across components like resistors).

Can this calculator handle parallel circuits?

No, this specific Kirchhoff’s Law Calculator is designed for a simple series circuit with one voltage source and up to three resistors. For series-parallel circuits or pure parallel circuits, the analysis is different, often involving KCL at nodes and KVL around loops.

What if my total resistance is zero?

If the total resistance (R1+R2+R3) is zero (or very close to it) and the voltage source is non-zero, this represents a short circuit. The current would theoretically be infinite, which in reality would blow a fuse or damage the source. The calculator will indicate a short circuit or very high current in such cases if R_total is 0 and V_s > 0.

Does this work for AC circuits?

This calculator is for DC circuits with resistors. For AC circuits with capacitors and inductors, impedance (Z) is used instead of resistance (R), and phase angles need to be considered. The principles of KVL and KCL still apply, but the math involves complex numbers.

Why is the KVL check not exactly zero?

It might be very slightly off zero due to rounding in the calculations and display. It should be a very small number if the inputs are valid.

What are the limitations of this calculator?

It’s for DC series circuits, up to 3 resistors, ideal components, and one source. It doesn’t handle non-linear elements, AC, or complex circuit topologies.

How do I find the power dissipated by each resistor?

The power (P) dissipated by a resistor is P = I² * R, or P = V * I, where I is the current through it and V is the voltage drop across it. The table in the calculator shows the power for each resistor.