Question

An alternating voltage (in volts) given by

$V = 200\sqrt{2}\sin(100t)$ is connected to $1\text{ }\text{μ}\text{F}$ capacitor through an ideal ac ammeter in series. The reading of the ammeter and the average power consumed in the circuit shall be

• A. 20 mA, 0
• B. 20 mA, 4W
• C. $\text{20}\sqrt{2}\text{ mA, 8 W}$
• D. $\text{20}\sqrt{2}\text{ mA, 4}\sqrt{2}\text{ W}$

Answer 1

Answer: (A)

20 mA, 0

Answer 2

: On comparing $V = 200\sqrt{2}\sin(100t)$ with

$V = V_{0}\sin\omega t,$ we get

$V_{0} = 200\sqrt{2}V,\omega = 100rads^{- 1}\therefore V_{rms} = \frac{V_{0}}{\sqrt{2}} = \frac{200\sqrt{2}V}{\sqrt{2}} = 200V$

The capacitive reactance is ,

$X_{C} = \frac{1}{\omega C} = \frac{1}{100 \times 1 \times 10^{- 6}} = 10^{4}\Omega$

ac ammeter reads the rms value of current, therefore, the reading of the ammeter is,

$I_{rms} = \frac{V_{rms}}{X_{C}} = \frac{200V}{10^{4}\Omega} = 20 \times 10^{- 3}A = 20mA$

The average power consumed in the circuit,

$P = I_{rms}V_{rms}\cos\varphi$

In an pure capacitive circuit, the phase difference between current and voltage is $\frac{\pi}{2}.$

$\therefore\cos\varphi = 0$

$\therefore P = 0$