Question

If instantaneous current is given by i = 4 cos (ω t + ∅) amperes, then the r.m.s. value of current is
(a) 4 amperes(b) 2√2 amperes(c) 4√2 amperes(d) Zero amperes

Answer 1

answer : option (b) 2√2 Ampere

explanation : standard equation of instantaneous current is given by, $I=I_0cos(\omega t+\Phi)$ .....(1)

where $I_0$ is peak value of current of an alternating circuit,$\omega$ is angular frequency, $\Phi$ is phase angle.

a/c to question, If instantaneous current is given by $I=4cos(\omega t+\Phi)$....(2)

compare equations (1) and (2),
$I_0=4$

To find rms value of current, use formula
$\quad I_{rms}=\frac{I_0}{\sqrt{2}}$

so, rms value of current = 4/√2 = 2√2 Amp