Question

Assume that there is three resistance (r1, r2, r3) and two batteries emfs are given as (five positive numbers). Using Kirchhoff’s node and loop law, set up a system of independent equations that would allow you to solve for all the currents for circuits. Note that there will be more than three unknown currents.

do not solve the system of equations , just list the equations. Make sure that all the three equations are independent of eachother and that there are as many equations as there are unknown.

Answer 1

Consider the network given below-

Using Kirchhoffs Current Law, KCL the equations are given as:

At node A :$I_1 + I_2 = I_3$

At node B :  $I_3 = I_1 + I_2$

Using Kirchhoffs Voltage Law, KVL the equations are given as:

Loop 1 is given as :  $10 = R_1 I_1 + R_3 I_3 = 10I_1 + 40I_3$

Loop 2 is given as :  $20 = R_2 I_2 + R_3 I_3 = 20I_2 + 40I_3$

Loop 3 is given as :  $10 – 20 = 10I_1 – 20I_2$