Kirchhoff Voltage Loop Solver
Sum of voltages around a closed loop = 0. Solve a 2-loop circuit with two batteries and three resistors.
Result
Loop currents
I₁ = 0.0437 A, I₂ = 0.0226 A
Branch through R₂: 0.0211 A.
- I through R₁0.0437 A
- I through R₂ (shared)0.0211 A
- I through R₃0.0226 A
- V across R₁4.3677 V
- V across R₂4.6323 V
- V across R₃10.6323 V
Step-by-step
- Loop 1 KVL: V₁ = R₁·I₁ + R₂·(I₁−I₂) → (100+220)·I₁ − 220·I₂ = 9.
- Loop 2 KVL: V₂ = R₃·I₂ + R₂·(I₂−I₁) → −220·I₁ + (220+470)·I₂ = 6.
- Solve 2x2: I₁ = 0.0437 A, I₂ = 0.0226 A.
How to use this calculator
- Enter the two battery voltages and three resistor values.
- Read both loop currents and the current through the shared middle resistor.
About this calculator
Kirchhoff's voltage law (KVL): the sum of voltage drops and rises around any closed loop is zero. For a circuit with two loops sharing a middle resistor, this gives two equations with two unknowns (the loop currents), solvable by determinant or substitution. The current through the shared resistor is the difference of the two loop currents.
Frequently asked
An imagined current circulating around a single loop. Real branch currents are sums or differences of loop currents (the shared resistor between two loops sees I₁ − I₂).
Related calculators
Ohm's Law Calculator (Extended)
V = IR, P = IV = I²R = V²/R. Pick which two values you know and solve for the others.
Parallel Resistance Calculator
1/R = 1/R₁ + 1/R₂ + … — find equivalent resistance of resistors in parallel.
Series Resistance Calculator
R_total = R₁ + R₂ + R₃ + … — find equivalent resistance of resistors in series.
Electrical Power Calculator
P = IV — compute power from voltage and current, or from voltage and resistance, or current and resistance.
Capacitance Calculator
C = Q/V or parallel-plate C = ε₀A/d. Compute capacitance, charge stored, or energy.
Inductance Calculator
L = μ₀N²A/ℓ for an ideal solenoid, or V = L(dI/dt) for the defining equation.