The time required for a 50 Hz sinusoidal altemating current to change its value from zero to the r.m.s. value

Question

The time required for a 50 Hz sinusoidal altemating current to change its value from zero to the r.m.s. value (A) 1.5 × 10-2 s (B) 2.5 × 10-3 s (C) 10-1 s (D) 10-6 s

Tardigrade Admin · Accepted Answer

I=I0 sin ω t I text rms =(I0/√2) So (I0/√2)=I0 sin ω t sin (π/4)= sin (2 π)(50) t (π/4)=2 π(50) t t=(1/400) s t=0.25 × 10-2 ⇒ 2.5 × 10-3 s

Q. The time required for a $50 Hz$ sinusoidal altemating current to change its value from zero to the r.m.s. value

$1.5 \times 1 0^{- 2} s$

$2.5 \times 1 0^{- 3} s$

$1 0^{- 1} s$

$1 0^{- 6} s$

$I = I_{0} sin ω t$
$I_{rms} = \frac{I _{0}}{2}$
So $\frac{I _{0}}{2} = I_{0} sin ω t$
$sin \frac{π}{4} = sin (2 π) (50) t$
$\frac{π}{4} = 2 π (50) t$
$t = \frac{1}{400} s$
$t = 0.25 \times 1 0^{- 2}$
$\Rightarrow 2.5 \times 1 0^{- 3} s$

Q. The time required for a 50Hz sinusoidal altemating current to change its value from zero to the r.m.s. value

1.5×10−2s

2.5×10−3s

10−1s

10−6s