Question

The voltage of an AC source varies with time according to the equation, $V=100\sin \left(100\pi t\right)\cos \left(100\pi t\right)$. If this voltage is applied across a resistor of $25\Omega$, then -

• A. Current flowing in the circuit is, $I=2\sin \left(200\pi t\right)$
• B. RMS value of current is $\sqrt{2}\text{A}$
• C. Current and voltage are in phase
• D. All of the above

Answer 1

The correct option is D All of the above

Given:

$V=100\sin \left(100\pi t\right)\cos \left(100\pi t\right)$

$\Rightarrow V=50\times \left(2\sin 100\pi t\cos 100\pi t\right)$

$\therefore V=50\sin \left(200\pi t\right)...\left(i\right)$

$[\because 2\sin \theta \cos \theta =\sin 2\theta ]$

The current is given by,

$I=\frac{V}{R}$

$\Rightarrow I=\frac{50\sin \left(200\pi t\right)}{25}$

$\Rightarrow I=2\sin \left(200\pi t\right)...\left(ii\right)$

From equations $\left(i\right)$ and $\left(ii\right)$, it is clear that voltage and current are in phase.

RMS value of current is,

$I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}\text{A}$

Hence, option $\left(D\right)$ is the correct answer.