Question

In each of the circuits shown, calculate the current through each resistor and potential difference across each resistor.

R-202 R=10Ω R,-10Ω R1=10Ω

Answer 1

For first circuit

Applying Kirchoffs Law

=>   20 - 10 = (I1 + I2 ) * 10 + 10 * I1 + 20 * I1

Also,   20 - 10 = (I1 + I2 ) * 10 + 15 * I2

=> I1 = 0.166 A

=> I2 = 0.33 A

=> current through R1 = 0.496 A            Potential difference = 4.96 V

=>   current through R2 = 0.33 A            Potential difference = 4.95 V

=>   current through R3 = 0.166 A            Potential difference = 1.66 V

=> current through R4 = 0.166 A            Potential difference = 3.32 V

For second circuit

Applying Kirchoffs Law

=>   20   = (I1 + I2 ) * 20 + 15 * I2 + 10 * I2

Also,   20 - 10 = (I1 + I2 ) * 20 + 10 * I1

=> I1 = 0.0526 A

=> I2 = 0.421 A

=> current through R1 = 0.0526 A            Potential difference = 0.526 V

=>   current through R2 = 0.421 A            Potential difference = 6.315 V

=>   current through R3 = 0.421 A            Potential difference = 4.21 V

=> current through R4 = 0.4736 A            Potential difference = 9.472 V

For third circuit

Applying Kirchoffs Law

=>   20   = (I1 + I2 ) * 20 + 15 * I2 + 10 * I2

Also,   20 - 10 = (I1 + I2 ) * 20 + 10 * I1

=> I1 = 0.0526 A

=> I2 = 0.421 A

=> current through R1 = 0.0526 A            Potential difference = 0.526 V

=>   current through R2 = 0.421 A            Potential difference = 6.315 V

=>   current through R3 = 0.421 A            Potential difference = 4.21 V

=> current through R4 = 0.4736 A            Potential difference = 9.472 V