$A$ sinusoidal voltage of peak value $283\,V$ and frequency $50\,Hz$ is applied to a series $LCR$ circuit in which $R = 3\,\Omega$,$L = 25.48\,mH$,and $C = 796\,\mu F$. Find the impedance of the circuit in $\Omega$.

When $100 \ V$ $d.c.$ is applied across a solenoid,a current of $1 \ A$ flows in it. When $100 \ V$ $a.c.$ is applied across it,the current drops to $0.5 \ A$. If the frequency is $50 \ Hz$,the impedance and inductance are:

The variation of impedance $Z$ of a series $\text{LCR}$ circuit with the frequency $f$ of the source is shown in the figure. Which of the following statement$(s)$ is/are true?

$A$ $10\, V, 60\, W$ bulb is to be connected to a $100\, V, 50\, Hz$ $AC$ source. To operate the bulb at its rated power,an induction coil is connected in series with it. Calculate the required self-inductance of the coil.

When alternating current is passed through an $L-R$ series circuit,the power factor is $\frac{\sqrt{3}}{2}$ and $R=50 \ \Omega$. If the frequency of the source is $50 \ Hz$,then the value of $L$ is (Assume $\pi \approx 3.14$):
$\left[\cos \frac{\pi}{6}=\frac{\sqrt{3}}{2}, \quad \sin \frac{\pi}{6}=\frac{1}{2}, \quad \tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}\right]$

An alternating current source of frequency $100\, Hz$ is connected to a combination of a resistor,a capacitor,and an inductor in series. The potential difference across the inductor,the resistor,and the capacitor is $46\, V$,$8\, V$,and $40\, V$ respectively. The electromotive force $(EMF)$ of the alternating current source in volts is: