In the circuit given below, the voltage across the 18 Ω resistor is 90 V. The voltage across the combined circuit is _________(a) 125 V(b) 16 V(c) 24 V(d) 40 VThis question was posed to me during an interview.Query is from Advanced Problems on Network Theory in section Network Theory and Complex Circuit Diagram of Network Theory

In the circuit given below, the voltage across the 18 Ω resistor is

1.	In the circuit given below, the voltage across the 18 Ω resistor is 90 V. The voltage across the combined circuit is _________(a) 125 V(b) 16 V(c) 24 V(d) 40 VThis question was posed to me during an interview.Query is from Advanced Problems on Network Theory in section Network Theory and Complex Circuit Diagram of Network Theory
Answer» The correct choice is (a) 125 V For explanation I would say: Current through the 18 Ω resistance = \(\frac{90}{18}\) = 5 A Equivalent resistance of 3 Ω and 7 Ω banks = \(\frac{3 × 6}{3 + 6}\) = 2 Ω Since, this 2 Ω resistance is in series with 18 Ω resistance, THEREFORE total resistance = 18 + 2 = 20 Ω This 20 Ω resistance is in parallel with 5 Ω resistance = \(\frac{5 × 20}{5 + 20}\) = 4 Ω Hence, total resistance of the circuit = 1 + 4 = 5 Ω Current through this BRANCH = 5 A ∴ Voltage across dc= 5 × 20 = 100 V Hence current through 5 Ω resistance = \(\frac{100}{5}\) = 20 A ∴ Total current = 20 + 5 = 25 A Since, total resistance of the circuit is 5 Ω therefore, voltage E = 25 × 5 = 125 V.

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