Question

A circuit consists of an excitation voltage VS, a resistor network and a resistor R. For different values of R, the values of V and I are as given, R = ∞, V = 5 volt; R = 0, I = 2.5 A; when R = 3 Ω, the value of V is __________

(a) 1 V

(b) 2 V

(c) 3 V

(d) 5 V

The question was asked in a national level competition.

My doubt stems from Advanced Problems Involving Complex Circuit Diagram topic in portion Network Theory and Complex Circuit Diagram of Network Theory

Answer 1

Correct choice is (c) 3 V

The explanation: When R = ∞, V = 5v,

Then, Voc = 5V and the circuit is open

When R = 0, I = 2.5A

Then, Isc = 2.5 and the circuit is short circuited.

So, Req = \(\frac{V_{OC}}{I_{SC}}\)

= \(\frac{5}{2.5}\) = 2 Ω

Hence the voltage across 3 Ω is 3 volt.