~(c) The root-mean-square (r.m.s.) value of an alternating current is the steady or direct current which produces the same heating effect per secoridin a given resistor. Its relationship with the peakvalue of alternating current \(I_{o}\)is given by
\(I_{r.m.s} = \frac{1}{\sqrt{2}} I_{o}\)
d(i) \(I\) is the instantaneous current
\(I_{o}\)is the peak value of the current
\(\alpha\)is the angular frequency
\(\alpha t\) is the phase or the current (since it is wave-like).
(ii) \(I = I_{o} \sin \alpha t\)
= \(I_{r.m.s} \sqrt{2} \sin 30°\)
= \(\sqrt{2} \times 15 \times \frac{1}{2} = 10.6A\)
