Kirchhoff's Laws Calculator: Two Sources and a Shared Resistor by the Node Voltage Method

Solve the two-battery circuit with Kirchhoff's laws and check the answer.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the voltage and series resistor of each source, and the shared resistor in the middle branch.

The calculator finds the voltage at the junction, then each current, then checks that the currents at the junction add up and the voltages round the loop add to zero.

Formulas used

  • V_N = \frac{V_1/R_1 + V_2/R_2}{1/R_1 + 1/R_2 + 1/R_3}
  • I_1 + I_2 = I_3
  • V_1 - I_1R_1 - I_3R_3 = 0

Worked example

With the default numbers in the calculator above:

  1. Voltage at the junction (node voltage method: the currents into the node add up to zero): 5.54 V
  2. Current from the first source: 1.62 A
  3. Current from the second source: 0.23 A
  4. Current in the shared resistor: 1.85 A
  5. Kirchhoff's current law at the junction: I1 + I2 = I3: I1 + I2 = 1.85 A and I3 = 1.85 A
  6. Kirchhoff's voltage law round the loop of the first source and the shared resistor: The voltages round the loop add to 0 V (zero)
  7. Power supplied by the sources and power lost in the resistors: 20.77 W in and 20.77 W in the resistors (they are equal)

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is Kirchhoff's current law?

The currents into a junction add up to the currents out of it.

What is Kirchhoff's voltage law?

The voltage rises and drops around any closed loop add up to zero.

Why is a current negative?

The real current flows the opposite way to the direction assumed, so that source is being charged.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any first-year electrical circuits text (Kirchhoff's laws, nodal analysis).

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