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An online calculator to solve Kirchhoff's equations in a dc circuit is presented. The calculator accepts any number of equations. The outputs are the values of all currents in the given circuit.

Write the voltages and Currents Equations Using Kirchhoff's

Example
Find all currents through the resistors in the circuit below, given the voltage sources \( e_1 = 20 \) V, \( e_2 = 5 \) V, and the resistances \( R_1 = 100 \; \Omega \) , \( R_2 = 120 \; \Omega \) and \( R_3 = 60 \; \Omega \).

step 1 - Use Kirchhoff's laws of voltages to write an equation for each cloed loop:
Loop L1: \( e_1 - R_1 i_1 - R_2 i_2 + e_2 = 0 \)
Loop L2: \( R_2 i_2 - R_3 i_3 = 0 \)
step 2: Use Kirchhoff's laws of currents to write an equation at each node:
Node A: \( i_1 - i_2 - i_3 = 0 \)
step 2 - Rearrange the equations so that terms depending on the unknowns are on the left and all constants on the right, and order the unknowns \( i_1, i_2 \) and \( i_3 \) in each equation:
\( \begin{array}{lclcl}
R_1 i_1 + R_2 i_2 & = & e_1 + e_2 \\
R_2 i_2 - R_3 i_3 & = & 0 \\
i_1 - i_2 - i_3 & = & 0 \end{array} \)
step 3 - Substitute all resistances of resistors and voltages of voltage sources by their numerical values and include all unknowns in the equations including the ones whose coefficents are zeros:
\( \begin{array}{lclcl}
100 \; i_1 + 120 \; i_2 + 0 \; i_3& = & 25 \\
0 \; i_1 + 120 i_2 - 60 i_3 & = & 0 \\
i_1 - i_2 - i_3 & = & 0 \end{array} \)
step 4 - Enter the number of equations \( m \) ( which is equal to the number of unknowns) and the coefficients of \( i_1, i_2 \) and \( i_3 \) into the calculator and find the currents:
Enter Number of Equations: \( m = \)

Change values of coefficients in above matrix (if needed) and click

More Activities

Find all currents through the resistors in the circuit below, given the voltage sources \( e_1 = 20 \) V, \( e_2 = 5 \) V, and the resistances \( R_1 = 100 \; \Omega \), \( R_2 = 120 \; \Omega \), \( R_3 = 60 \; \Omega \), \( R_4 = 40 \; \Omega \), \( R_5 = 240 \; \Omega\) and \( R_6 = 80 \; \Omega \).

Note: The circuit has 4 loops and 3 nodes which gives 7 equations with 7 unknowns \( i_1, i_2 ,...., i_7 \)
The solution to this activity is in Solve DC Circuits Problems , problem 3.