Question

Time required for a 50 hz sinusoidal alternating current to change its value from zero to r.m.s. value is?

Answer 1

i = current at any time "t" in the circuit

i₀ = maximum value of the current in the circuit

f = frequency of the alternating current = 50 Hz

current at any time is given as

i = i₀ Sin(2πft)

given that : i = rms current = i₀/(√2)

hence i₀/(√2) =  i₀ Sin(2πft)

Sin(2πft) = 1/(√2)

2πft = π/4

2(50)t = 1/4

t = 1/400 sec

t = 2.5 x 10⁻³ sec

hence time taken is given as 2.5 x 10⁻³ sec

Answer 2

We know that,

I = i• sin (2πft) - - - (1)

And, I = i•/√2 - - - (2)

From (1) and (2),

We get,

i•/√2 = i• sin (2πft) - - - {i• gets cancelled out}

Therefore,

1/√2 = sin (2πft)

=> π/4 = 2πft - - - {π gets cancelled out}

We get,

1/4 = 2 x 50 x t (here, f = 50, given)

Or, t = 1/400 = 2.5 x 10^-³ seconds ------ (10 to power minus three)

I hope it helped. :)