Question

In the circuit shown below what is the value of RL for which maximum power is transferred to RL?

(a) 2.4 Ω

(b) \(\frac{8}{3}\) Ω

(c) 4 Ω

(d) 6 Ω

This question was addressed to me in an interview for job.

This intriguing question comes from Advanced Problems on Millman’s Theorem and Maximum Power Transfer Theorem topic in portion Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Right option is (c) 4 Ω

The explanation is: Maximum power is transferred to RL when the load resistance equals the Thevenin resistance of the circuit.

RL = RTH = \(\frac{V_{OC}}{I_{SC}} \)

Due to open-circuit, VOC = 100 V; ISC = I1 + I2

Applying KVL in lower loop, 100 – 8I1 = 0

Or, I1 = \(\frac{100}{8} = \frac{25}{2}\)

And VX = -4I1 = -4 × \(\frac{25}{2}\) = -50V

KVL in upper loop, 100 + VX – 4I2 = 0

I2 = \(\frac{100-50}{4} = \frac{25}{2}\)

Hence, ISC = I1 + I2 = \(\frac{25}{2} + \frac{25}{2}\) = 25

RTH = \(\frac{V_{OC}}{I_{SC}} = \frac{100}{25}\) = 4 Ω

RL = RTH = 4 Ω.