Kirchhoff's Voltage Law (KVL)

ΣV = V₁ + V₂ + V₃ + ... = 0

Quick answer

This calculator solves ΣV = V₁ + V₂ + V₃ + ... = 0 for ΣV. With Voltage Drops 12 V, 26.4 V, 56.4 V, the result is 94.8.

Calculator

Result
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Formula

ΣV = V₁ + V₂ + V₃ + ... = 0

Description

Kirchhoff's Voltage Law states that the algebraic sum of all voltages around any closed loop in a circuit must equal zero. This is a consequence of the conservation of energy: a charge traveling around a closed loop must return to its starting potential. Voltage sources are positive (energy added) and voltage drops across resistors and other components are negative (energy consumed). KVL is one of the two fundamental laws (along with KCL) used in systematic circuit analysis methods like mesh analysis and loop analysis.

Variables

  • V₁, V₂, V₃... — Voltages around the loop (V), with sign convention: positive for rises, negative for drops

Practical Notes

Enter all voltage rises as positive values and all voltage drops as negative values. The result should be zero (or very close) for a valid circuit loop. A non-zero sum indicates a measurement error or a missing voltage source/drop in the analysis. KVL applies to any closed path, not just physical component loops.

Symbols and units

Symbol Meaning Default unit Accepted units
values Voltage Drops V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Voltage Drops 12 V, 26.4 V, 56.4 V
  2. 2. The relation: ΣV = V₁ + V₂ + V₃ + ... = 0
  3. 3. Substitute: values = 12 V, 26.4 V, 56.4 V
  4. 4. Result: ΣV = 94.8

Totals for common combinations

Components Values Total
2 12 V + 12 V 24 V
2 12 V + 26.4 V 38.4 V
2 12 V + 120 V 132 V
3 12 V + 12 V + 12 V 36 V
3 12 V + 26.4 V + 56.4 V 94.8 V
4 12 V + 12 V + 12 V + 12 V 48 V
4 12 V + 26.4 V + 56.4 V + 120 V 0.2148 kV
5 12 V + 12 V + 12 V + 12 V + 12 V 60 V

Worked examples

Minimum range

Given: Voltage Drops 12 V, 26.4 V, 56.4 V

Result: ΣV = 94.8

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Frequently asked questions

How do you calculate Kirchhoff's Voltage Law (KVL)?

Use ΣV = V₁ + V₂ + V₃ + ... = 0. With Voltage Drops 12 V, 26.4 V, 56.4 V, ΣV works out to 94.8.

What is the formula for Kirchhoff's Voltage Law (KVL)?

The formula is ΣV = V₁ + V₂ + V₃ + ... = 0. Kirchhoff's Voltage Law states that the algebraic sum of all voltages around any closed loop in a circuit must equal zero.

Related Concepts

All Basic Electronics formulas →
Ohm's Law Electrical Power Voltage Divider Current Divider Thévenin Equivalent Norton Equivalent Temperature Coefficient of Resistance Kirchhoff's Voltage Law (KVL)

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