In an ac circuit, the instantaneous value of current (in A) and voltage (in V) are given as \( I = 5\sin\omega t \) and \( V = 200\cos\left(\omega t + \displaystyle\frac{\pi}{3}\right) \), respectively. The phase difference between voltage and current is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{5\pi}{6} \)
A phase difference can be read off only when both quantities are written with the same trigonometric function. Convert the cosine into a sine using \( \cos x = \sin(x + \pi/2) \).
\( \displaystyle V = 200\sin\left(\omega t + \frac{\pi}{3} + \frac{\pi}{2}\right) \)
\( \displaystyle V = 200\sin\left(\omega t + \frac{5\pi}{6}\right) \)
The current \( I = 5\sin\omega t \) has phase \( \omega t \), so the voltage leads the current by
\( \displaystyle \phi = \frac{5\pi}{6} \)