# Linear Equation Solver: Electric Circuits

Description| How it works| Electric CircuitsLinear Equations appear in many situations, a common applications of linear equations is in working out voltages and currents using Kirchoff's Laws. We will use the Linear Equation solver to work out the currents in the circuit shown below:

We have V

_{1}= 10 V, V

_{2}= 2 V, R

_{1}= 6 Ω, R

_{2}= 8 Ω and R

_{3}= 4 Ω.

According to Kirchoff's current law, we have

i

_{1}= i

_{2}+ i

_{3}or

i

_{1}- i

_{2}- i

_{3}= 0

Now we use Kirchoff's voltage law, for the loop on the left (going in a clockwise direction), we have

-i

_{1}R

_{1}- i

_{2}R

_{2}+ V

_{1}= 0

We assume voltage to be positive when moving from the negative to positive pole of the battery. (This choice of directions and signs is abitrary, but it has to be used consistently.)

Putting in the values, we have

6i

_{1}+ 8i

_{2}= 10

Similarily, for the loop on the right, we have

-4i

_{3}- 2 + 8i

_{2}= 0 or

8i

_{2 }- 4i

_{3}= 2

Subsitituting these in the Linear Equation Solver, we get

Therefore, we have

i

_{1}= 1 A

i

_{2}= 0.5 A

i

_{3}= 0.5 A