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GATE 2015 EE – Question 55

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 2 marks · Numerical answer

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in Volt) is given by $v(t) = 12\sin t$. If the circuit is in steady state, then the rms value of the current (in Ampere) flowing in the circuit is ________.

An AC source $v(t)$ and an 8 V DC battery in series with a $1\ \Omega$ resistor and a 1 H inductor.

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Correct answer: 9.9 to 10.1

Explanation

The DC part drives $\frac{8}{1} = 8$ A, since the inductor is a short for DC. The AC part has an impedance of $1 + j1$ with magnitude $\sqrt{2}$, so its peak current is $\frac{12}{\sqrt{2}} = 8.485$ A and its rms value is $\frac{8.485}{\sqrt{2}} = 6$ A. The total rms current is $\sqrt{8^2 + 6^2} = 10$ A.