Question

What is the power loss in the 10 Ω resistor in the network shown in the figure below?

(a) 15.13 W

(b) 11.23 W

(c) 16 W

(d) 14 W

The question was asked by my college director while I was bunking the class.

Question is from Advanced Problems on Network Theorems in section Useful Theorems in Circuit Analysis of Network Theory

Answer 1

The correct choice is (a) 15.13 W

The explanation: In mesh aef, 8(I1 – I3) + 3(I1 – I2) = 15

Or, 11 I1 – 3 I2 – 8I3 = 15

In mesh efd, 5(I2 – I3) + 2I2 + 3(I2 – I1) = 0

Or, -3 I1 + 10I2 – 5I3 = 0

In mesh abcde, 10I3 + 5(I3 – I2) + 8(I3 – I1) = 0

Or, -8I1 – 5I2 +23I3 = 0

Thus loop equations are,

11 I1 – 3 I2 – 8I3 = 15

-3 I1 + 10I2 – 5I3 = 0

-8I1 – 5I2 + 23I3 = 0

Solving by Cramer’s rule, I3 = current through the 10Ω resistor = 1.23 A

∴ Current through 10 Ω resistor = 1.23 A

Power loss (P) = \(I_3^2 r\) = (1.23)^2×10 = 15.13 W.