Question

In the circuit given below, the value of R in the circuit, when the current is zero in the branch CD is _________

(a) 10 Ω

(b) 20 Ω

(c) 30 Ω

(d) 40 Ω

This question was addressed to me in exam.

Query is from Advanced Problems on Network Theory topic in chapter Network Theory and Complex Circuit Diagram of Network Theory

Answer 1

Right option is (d) 40 Ω

Explanation: The current in the branch CD is zero if the potential difference in the branch CD is zero.

That is, VC = VD

Or, V10 = VC = VD = VA × \(\frac{10}{15}\)

VR = VA × \(\frac{R}{20+R} \)

And V10 = VR

∴ VA × \(\frac{10}{15}\) = VA × \(\frac{R}{R+20} \)

∴ R = 40 Ω.