Question

A circuit is given in the figure below. We can infer that ________

(a) The circuit follows Reciprocity Theorem

(b) The circuit follows Millman’s Theorem

(c) The circuit follows Superposition Theorem

(d) The circuit follows Tellegen Theorem

This question was posed to me in quiz.

This key question is from Advanced Problems on Reciprocity Theorem in division Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Correct choice is (a) The circuit follows Reciprocity Theorem

Easiest explanation: Let us consider this circuit,

Equivalent Resistance, Equivalent Resistance, REQ = 20 + [60 || 30]

= 20 + \(\frac{60 × 30}{60+30}\)

= 20 + 20 = 40 Ω

Total current from the source, I = \(\frac{120}{40}\) = 3A

Now, by using current division rule, I1 = \(\frac{3 × 60}{30+60}\) = 2 A.

Again, let us consider this circuit,

Equivalent resistance, REQ = [[20 || 60] + 30]

= \(\Big[\frac{20 × 60}{20+60} + 30\Big]\)

= [15 + 30] = 45 Ω

Total current = \(\frac{120}{45}\) = 2.67 A

Current through the 20Ω resistor is, I2 = \(\frac{2.67 × 60}{60+20}\) = 2 A

Since I1 = I2, the circuit follows Reciprocity Theorem.