First slide

Power in a.c. circuit

Question

Current through a circuit containing R and L or R and C or C and L is
$(\cos 100 π t - \sqrt{3} . \sin 100 π t) A m p .$
Voltage applied across the combination is $100 \cos 100 π t v o l t .$ Then power consumed by the circuit is

Easy

A

$50 \sqrt{3} W$
B

$25 \sqrt{3} W$
C

50 W
D

70 W

Solution

(3)
$\begin{array}{l} i = 2 (\cos 100 π t . \frac{1}{2} - \sin 100 π t . \frac{\sqrt{3}}{2}) A = 2 \cos (100 π t + \frac{π}{3}) A \\ υ = 100 \cos 100 π t v o l t . \\ ∴ P o w e r P = (\frac{2}{\sqrt{2}}) (\frac{100}{\sqrt{2}}) \cos \frac{π}{3} w a t t = 50 W \end{array}$

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