Question

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

• A. rms value of current is 5 A
• B. mean value of this current in one half period will be $\frac{6}{\pi }$
• C. If voltage applied is $V=V_{m}sin\omega t$, then the circuit must be containing resistance and capacitance.
• D. If voltage applied is $V=V_{m}sin\omega t$, the circuit may contain resistance and inductance

Answer 1

The correct option is C If voltage applied is $V=V_{m}sin\omega t$, then the circuit must be containing resistance and capacitance.

$i=3sin\omega t+4cos\omega t$
$=5[\frac{3}{5}sin\omega t+\frac{4}{5}cos\omega t]$
$=5\left[sin\right(\omega t+\delta \left)\right]\left(1\right)$
$\Rightarrow$ rms value
$=\frac{5}{\sqrt{2}}\Rightarrow$
$\Rightarrow$ mean value
$\frac{{\int }_{T_1}^{T_2}dt}{{\int }_{T_1}^{T_2}dt}$
$\therefore$ Initial value of time is not given hence the mean value will be different for various time intervals. If voltage applied is $V=V_{m}sin\omega t$ then i given by equation (1) indicates that it is ahead of V by $\delta$ where 0 < $\delta$ < 90 which indicates that the circuit contains R & C.