Question

Current in an ac circuit is given by $I=3\sin \omega t+4\cos \omega t$, then

• A. RMS value of current is $5A$
• B. Mean value of this current in any one half period will be $6\pi$
• C. If voltage applied is $V=V_m\sin \omega t$, then the circuit may be containing resistance and capacitance only
• D. If voltage applied is $V=V_m\sin \omega t$, the circuit may contain resistance and inductance only

Answer 1

The correct option is C If voltage applied is $V=V_m\sin \omega t$, then the circuit may be containing resistance and capacitance only

$I=3sin\omega t+4cos\omega t$
$\Rightarrow I=5(\frac{3}{5}sin\omega t+\frac{4}{5}cos\omega t)$
$\Rightarrow I=5sin(\omega t+\alpha )$ $;\alpha =ta{n}^{-1}\frac{4}{5}$
therefore,
rms value of current = $5/\sqrt{2}A$
Mean value of current one half period = $\frac{1}{\pi }{\int }_0^{\pi }5sin\theta d\theta =\frac{1}{\pi }5{|-cos\theta |}_0^{\pi }=\frac{10}{\pi }A$
The current lags the voltage by an angle $\theta$, therefore the circuit may contain resistance and capacitor only.