First slide

Alternating current and voltage

Question

A resistance of 20 ohms is connected to a source of an alternating potential $V = 220 \sin (100 πt)$ The time taken by the current to change from its peak value to r.m.s. value is

Moderate

A

0.2 sec
B

0.25 sec
C

$25 \times 10^{- 3} \sec$
D

$2.5 \times 10^{- 3} \sec$

Solution

Peak value to r.m.s. value means current becomes $\frac{1}{\sqrt{2}}$ times.
So from $i = i_{0} \sin 100 πt \Rightarrow \frac{1}{\sqrt{2}} \times i_{0} = i_{0} \sin 100 πt$
$\Rightarrow \sin \frac{π}{4} = \sin 100 πt \Rightarrow t = \frac{1}{400} \sec = 2 .5 \times 10^{- 3} \sec$

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