First slide

Alternating Current and voltage

Question

An AC source rated 220 V, 50 Hz is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

Moderate

A

0.25 ms
B

25 ms
C

2.5 ms
D

2.5s

Solution

$L e t s a y i = i_{0} \cos (ω t) A t t = 0, i = i_{0} N o w, p u t i = i_{r m s} = \frac{i_{0}}{\sqrt{2}} \Rightarrow \frac{i_{0}}{\sqrt{2}} = i_{0} \cos (ω t) \Rightarrow ω t = \frac{π}{4} \Rightarrow t = \frac{π}{4 ω} = \frac{π}{4 (2 π f)} = \frac{1}{400} \Rightarrow t = 2.5 m s$

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