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

I have been asked this question in an interview.

Asked question is from Advanced Problems on Reciprocity Theorem topic in section Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Correct choice is (a) The circuit follows Reciprocity Theorem

The explanation: Let us consider this circuit,

Equivalent Resistance REQ = 20 + [30 || (20 + (20||20))]

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

= 20 + [30 || (20+10)]

= 20 + [30 || 30]

= 20 + \(\frac{30 × 30}{30+30}\)

= 20 + 15 = 35 Ω

The current drawn by the circuit = \(\frac{200}{35}\) = 5.71 A

Now, by using current division rule, we get, I1 = 1.43 A

Again, let us consider this circuit,

Equivalent Resistance, REQ = [[((30 || 20) + 20) || 20] + 20]

= \(\Big[\Big[\left(\left(\frac{30 × 20}{30+20}\right) + 20\right) || 20\Big] + 20\Big]\)

= [[(12 + 20) || 20] + 20]

= [[32 || 20] + 20]

= \(\Big[\left(\frac{32 × 20}{32+20}\right) + 20\Big]\)

= [12.31 + 20] = 32.31 Ω

The current drawn by the circuit = \(\frac{200}{32.31}\) = 6.19 A

Now, by using current division rule, we get, I2 = 1.43 A.

Since I1 = I2, the circuit follows Reciprocity Theorem.