The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volts) is given by v(t) = 12 sin t - General NAT GATE EE 2015 Question Paper (07-Feb-2015) (Shift 1) | ExamTest.live

mediumNATGATE EE 2015 Question Paper (07-Feb-2015) (Shift 1)General

1 attempts100% success rate1 mark

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volts) 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 ____.

Correct Answer

9.9-10.1

Solution & Step-by-step Explanation

Concept: Z(s) = R+ jX_{L} Where R = Resistance X_{L} = Inductive reactance Admittance is the inverse of impedance. Y (S) = \frac{1}{Z ( S )} = \frac{1}{( R + jω L )} Y (S) = \frac{1}{R ^{2} + ( ω L ) ^{2}} ∠ - t a n^{- 1} (ω L / R) V(t) = I(t) Z(s) I (t) = \frac{V ( t )}{Z ( s )} I(t) = V(t) Y(s) Explanation: Given R = 1Ω L = 1H ω = 1 rad/sec DC voltage = 8 V AC voltage = 12 sin t Total input voltage: Vᵢₙ(t) = 8 + 12 sin t I(t) = V(t) Y(s) As 8 V is DC voltage so frequency is equal to zero. i (t) = 8 \cdot \frac{1}{1 + 0} ∠ - t a n^{- 1} (0) + \frac{12}{1 + 1} sin (t - 4 5^{\circ}) i (t) = 8 + \frac{12}{2} (s in \cdot \frac{1}{2} - cos t \frac{1}{2}) I(t) = 8 + 6 sin t - 6 cos t I_{r m s} = 8^{2} + (\frac{6}{2})^{2} + (\frac{6}{2})^{2} = 10 A **I_{r m s} = 10 A**

Try it yourself before checking the explanation above.

The circuit shown in the figure has two sources connected in series. The instantaneous voltage of the AC source (in volts) 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 ____.