Question

In the circuit given below, the maximum power delivered to the load is ___________

(a) 3 W

(b) 5.2 W

(c) 3.2 W

(d) 4.2 W

The question was posed to me in an interview for internship.

The origin of the question is Advanced Problems on Reciprocity Theorem topic in chapter Useful Theorems in Circuit Analysis of Network Theory

Answer 1

The correct option is (d) 4.2 W

To explain I would say: Equivalent resistance of the circuit is = [{(3 + 2) || 5} + 10]

= (2.5 + 10) = 12.5 Ω

Total current drawn by the circuit is IT = \(\frac{50}{12.5}\) = 4 A

Current in 3 Ω resistor is I3 = IT ×  \(\frac{5}{5+5} = \frac{4 × 5}{10}\) = 2 A

VTH = V3 = 3 × 2 = 6V

RTH = RAB = [(2 + 5) || 3] = 2.1 Ω

For maximum power transfer RL = RTH = 2.1 Ω

∴ Current drawn by RL is IL = \(\frac{6}{2.1+2.1} = \frac{6}{4.2}\) = 1.42 A

∴ Power delivered to the load = \(I_L^2 R_L\)

= (1.42)^2(2.1) = 4.2 W.