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:

A
0.25 ms
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B
25 ms
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C
2.5 ms
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D
2.5 s
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Solution

## The correct option is C 2.5 msGiven, Vrms=200 V and f=50 Hz So, V0=220√2 V and ω=2πf=100π ⇒V=V0sinωt=220√2sin(100πt) Current in the resistor, I=I0sin100πt where I0=220√2R Let current is maximum for first time at time t1: I0=I0sin(100πt1) 1=sin(100πt1) π2=100πt1 t1=1200 Suppose that current is at its RMS value for first time at time t2: I0√2=I0sin(100πt2) 1√2=sin(100πt2) π4=100πt2 t2=1400 Δt=t1−t2=1200−1400 Δt=1400 s=2.5 ms

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