Electromagnetic Induction and Alternating Current 6 Question 5
####5. In an $\mathrm{AC}$ circuit, the instantaneous emf and current are given by $e=100 \sin 30 t, i=20 \sin 30 t-\frac{\pi}{4}$
In one cycle of $\mathrm{AC}$, the average power consumed by the circuit and the wattless current are, respectively (2018 Main)
(a) 50,0
(b) 50,10
(c) $\frac{1000}{\sqrt{2}}, 10$
(d) $\frac{50}{\sqrt{2}}, 0$
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Answer:
Correct Answer: 5. (c)
Solution:
- $\langle P\rangle=e_{\mathrm{rms}} i_{\mathrm{rms}} \cos \varphi=\frac{e_{0}}{\sqrt{2}} \frac{i_{0}}{\sqrt{2}} \cos \varphi$
$$ =\frac{e_{0} i_{0}}{2} \cos \varphi=\frac{(100)(20) \cos \frac{\pi}{4}}{2}=\frac{1000}{\sqrt{2}} \mathrm{~W} $$
Wattless current $=I_{\mathrm{rms}} \sin \varphi=\frac{20}{\sqrt{2}} \cdot \frac{1}{\sqrt{2}}=10 \mathrm{~A}$
