Physics · Reactance and impedance, LCR series circuit, resonance, power in AC circuits, wattless current
an circuit, the instantanceous emf and current are given by \) In one cycle of t
\( \ln \) an \( A C \) circuit, the instantanceous emf and current are given by \( e=100 \sin 30 t, i=\sin \left(30 t \frac{\pi}{4}\right) \) In one cycle of \( A C, \) the average power consumed by the circuit and the wattles current are, respectively
- A. 50,0
- B. 50,10
- C. \( \frac{1000}{\sqrt{2}}, 10 \)
- D. \( \frac{50}{\sqrt{2}}, 0 \)
Step-by-step solution
The average power consumed in an AC circuit is given by P_avg = V_rms I_rms cos φ. Here, assuming the phase difference φ = 0 (since the current expression likely has no phase shift), V_rms = 100/√2, I_rms = 1/√2, cos φ = 1, so P_avg = (100/√2)(1/√2) = 50 W. Wattless current is I_rms sin φ = 0. Thus, the answer is (50, 0).
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