Kirchhoff Law Calculator
Simple KCL/KVL solver for small linear circuits (sum of currents/voltage loops).
Enter Values
Fill in the fields and press Calculate to see instant results.
What is the Kirchhoff Law Calculator?
The Kirchhoff Law Calculator applies Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL) to analyze circuits. These fundamental principles state that the sum of currents entering a node equals the sum leaving it (KCL), and the sum of voltages around a closed loop equals zero (KVL). This calculator helps verify circuit behavior and solve for unknown currents and voltages in complex circuits.
Formula
Kirchhoff's Current Law (KCL):
The sum of currents entering a node equals the sum of currents leaving the node.
Kirchhoff's Voltage Law (KVL):
The sum of all voltage rises and drops around a closed loop equals zero.
How to Use
- For KCL Analysis: Enter the currents entering the node
- The calculator sums all input currents
- Enter currents leaving to verify KCL
- For KVL Analysis: Enter voltage drops around a loop
- The calculator verifies that the sum equals zero
Worked Example
KCL Example - Node Analysis:
- Current I₁ entering node = 5 A
- Current I₂ entering node = 3 A
- Current I₃ leaving node = ?
Calculation:
I₁ + I₂ = I₃
5 A + 3 A = 8 A
Result: Current I₃ leaving the node must be 8 A to satisfy KCL
Real-World Applications
- Circuit Verification: Verify that circuits are correctly designed by checking current conservation
- Node Voltage Analysis: Solve for unknown voltages and currents in multi-loop circuits
- Power Distribution: Analyze how power splits between parallel branches
- Fault Analysis: Identify circuit failures by detecting when KCL or KVL is violated
- Network Design: Plan distribution networks with multiple sources and loads
Key Definitions
- Node: A junction point in a circuit where three or more components meet
- Loop: A closed path through a circuit
- Kirchhoff's Current Law (KCL): The sum of currents entering a node equals the sum leaving (current conservation)
- Kirchhoff's Voltage Law (KVL): The sum of voltages around a closed loop equals zero (energy conservation)
- Branch: A single component or series of components between two nodes
- Mesh: A loop with no other loops inside it
Frequently Asked Questions
What is Kirchhoff's Current Law?
KCL states that the algebraic sum of currents at any node in a circuit must equal zero. This represents conservation of charge—current cannot accumulate at a node.
What is Kirchhoff's Voltage Law?
KVL states that the sum of voltages around any closed loop in a circuit equals zero. This represents energy conservation—energy provided by sources equals energy consumed by components.
How do I apply KCL to analyze circuits?
Identify all nodes in the circuit, sum currents entering and leaving each node, and set them equal. Use KCL equations along with Ohm's Law to solve for unknown currents and voltages.
How do I apply KVL to analyze circuits?
Trace a closed loop through the circuit, sum all voltage rises and drops (with appropriate signs), and set the sum to zero. Use KVL equations to solve for unknown voltages.
What's the difference between nodal and mesh analysis?
Nodal analysis uses KCL to write equations for each node, focusing on voltages. Mesh analysis uses KVL to write equations for each mesh (loop), focusing on currents. Both methods can solve the same circuit.
Can Kirchhoff's Laws be applied to AC circuits?
Yes, Kirchhoff's Laws apply to both DC and AC circuits. For AC circuits, use phasor representations of voltages and currents to account for phase relationships.