Practice portal › Alternating Current › Alternating Quantities: RMS and Mean

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

Asked in GUJCET 2009 · Instantaneous values and timing

Answer: (1) 2.5 ms

Step-by-step solution

Given: f=50 Hz, so the period is T=1/(50) s=20 ms.

Idea: starting from zero, I=I₀ sin ω t, and the rms value is (I₀)/(√2).

I₀ sin ω t=(I₀)/(√2)⇒sin ω t=1/(√2)⇒ω t=π/4.

t=π/(4ω)=π/(4×2π f)=1/(8f)=T/8=(20 ms)/8=2.5 ms.

So the time is 2.5 ms.

Why the other options are wrong

More Alternating Quantities: RMS and Mean questionsAll Alternating Quantities: RMS and Mean questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer