The domestic power supply of 220 V, 50 Hz is connected to a resistor. What is the time taken by the alternating current flowing in the resistor, to change from its maximum value to turns value?

Options

A. `5 xx 10^(-3) s`
B. `2.5 xx 10^(-3) S`
C. `10 xx 10^(-3) S`
D. `2.5 xx 10^(3)S`

Answer

D

Explanation

Suppose that at time `t_(1) = 0, i=i_(max)` and
`i_(rms) = (i_0)/(sqrt(2)) = i_(0) sin omega t_(2)`
`:. Sin omega t_(2) = 1/(sqrt2) :. Omega t_(2) = (pi)/4 :. t_(2) = (pi)/(4 omega)`
`:. t_(2) - t_(1) = (pi)/(4 omega)`
`=(pi)/(4 xx 2 pi f) = 1/(8 xx 50 ) = 1/400`
`:. t_(2)-t_(1) = 2.5 xx 10^(-3) s`.