$A$ direct current of $5\,A$ is superposed on an alternating current $I = 10 \sin \omega t$ flowing through a wire. The effective value of the resulting current will be

What are $A.C.$ signals?

The instantaneous voltages at three terminals marked $X, Y$ and $Z$ are given by
$V_x = V_0 \sin \omega t$
$V_y = V_0 \sin \left(\omega t + \frac{2 \pi}{3}\right)$
$V_z = V_0 \sin \left(\omega t + \frac{4 \pi}{3}\right)$
An ideal voltmeter is configured to read the $rms$ value of the potential difference between its terminals. It is connected between points $X$ and $Y$ and then between $Y$ and $Z$. The reading$(s)$ of the voltmeter will be:
$[A]$ $V_{XY}^{rms} = V_0 \sqrt{\frac{3}{2}}$
$[B]$ $V_{YZ}^{rms} = V_0 \sqrt{\frac{1}{2}}$
$[C]$ $V_{XY}^{rms} = V_0$
$[D]$ independent of the choice of the two terminals

The $ rms $ value of current in a $ 50 \,Hz $ $ AC $ circuit is $ 6 \,A $. The average value of $ AC $ current over a complete cycle is:

$A$ standard filament lamp consumes $100\,W$ when connected to $200\,V$ $AC$ mains supply. The peak current through the bulb will be $........\,A$.

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. Then the effective value ($RMS$ value) of the current is: