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In the circuit shown below find the power dissipated by 2Ω resistor.

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In the circuit shown below find the power dissipated by 2Ω resistor.

(a) 16.24

(b) 17.24

(c) 18.24

(d) 19.24

This question was posed to me during an internship interview.

My query is from Nodal Analysis in portion Steady State AC Analysis of Network Theory

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Correct answer is (c) 18.24

To explain I would say: Applying nodal analysis at node ‘a’, (Va-20∠30^o)/3+Va/(-j4)+Va/(2+j5)=0. On solving, Va = 16.27∠18.91⁰. Current in 2Ω resistor I2 = Va/(2+j5) = (16.27∠18.91^o)/(5.38∠68.19^o)=3.02∠-49.28^o. Power dissipated in 2Ω resistor P=I2^2 R=3.02^2×2 = 18.24W.

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