Question

Equation of alternating current is given by I= 10√2sin(100πt+π/6). The time taken by current to reach the root mean square value from t=0 is t'. Then the value of t' is ?

Answer 1

Instantaneous value of current
I = 10√2 sin(100πt + π/6)

[ general equation is I=Io×sin(wt+ phi ) ; where phi is the phase ]

Peak velue of current
Io= 10√2 A
RMS value of current
Irms = Io/√2 A
= (10√2 A)/√2 = 10 A ----(1)
Let t' be the time taken by the current to
reach the RMS value.
Irms = 10√2 sin(100π t' + π/6) ----(2)
Equating (1) and (2) we get
10√2 sin(100π t' + π/6) = 10
⇒ sin(100π t' + π/6)
= 1/√2 = sin (π/4)
⇒ 100π t' + π/6 = π/4
⇒ 100 t' = 1/1
∴ t' = (1/1200) s = 0.8×10^-3 s
=0.8 milli seconds