What is Kirchhoff’s Law?

Kirchhoff's Laws are fundamental principles in electrical engineering used to determine the distribution of voltage and current in complex circuits. They were developed by Gustav Kirchhoff in 1845. There are two primary laws: the Kirchhoff's Current Law (KCL) and the Kirchhoff's Voltage Law (KVL).

Kirchhoff’s Voltage Law (KVL)

KVL states that the algebraic sum of all electrical potential differences (voltages) around any closed loop or network is equal to zero. This is a direct application of the law of conservation of energy. In practice, this means the sum of the electromotive forces (EMF) is equal to the sum of the potential drops (I × R) across the resistors in the loop.

How to Use This Calculator

This calculator solves a common 2-mesh circuit problem. To get the result:

• Enter V1 and V2: These are the voltage sources in Loop 1 and Loop 2 respectively.
• Enter R1 and R2: The series resistors in the outer branches of the loops.
• Enter R3: The shared resistor located in the middle branch that both currents pass through.
• Click "Calculate" to see the simultaneous equations generated and the step-by-step solution for I1 and I2.

Frequently Asked Questions

Q: What if my current result is negative?
A: A negative current simply means the actual direction of current flow is opposite to the direction you assumed when setting up the equations. The magnitude remains correct.

Q: Can KVL be applied to AC circuits?
A: Yes, KVL applies to both DC and AC circuits, although for AC, you must use complex numbers (impedance) instead of simple resistance.