First slide

Alternating Current and voltage

Question

A group of electric lamps having a total power rating of 1000 watt is supplied by an ac voltage $E = 200 \sin (310 t + 60 °)$ . Then the r.m.s. value o the circuit current is

Moderate

A

10 A
B

$10 \sqrt{2} A$
C

20 A
D

$20 \sqrt{2} A$

Solution

$P = \frac{1}{2} V_{0} i_{0} cosφ \Rightarrow 1000 = \frac{1}{2} \times 200 \times i_{0} \cos 60^{o}$
$\Rightarrow i_{0} = 20 A \Rightarrow i_{rms} = \frac{i_{0}}{\sqrt{2}} = \frac{20}{\sqrt{2}} = 10 \sqrt{2} A .$

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