In the circuit shown,the power factor of the circuit is $1$ and the power factor of the box is $\frac{3}{5}$. Find the reading of the ammeter in $A$.

In an electrical circuit,$R$,$L$,$C$,and an $a.c.$ voltage source are all connected in series. When $L$ is removed from the circuit,the phase difference between the voltage and the current in the circuit is $\frac{\pi}{3}$. If instead $C$ is removed from the circuit,the phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $(\tan \frac{\pi}{3} = \sqrt{3})$.

$A$ transmitting station releases waves of wavelength $960\, m$. $A$ capacitor of $2.56\, \mu F$ is used in the resonant circuit. The self-inductance of the coil necessary for resonance is $............ \times 10^{-8}\, H$.

$A$ series $AC$ circuit consists of an inductor and a capacitor. The inductance and capacitance are $1 \ H$ and $25 \ \mu F$ respectively. If the current is maximum in the circuit,then the angular frequency will be:

In the circuit shown in the figure, the ratio of the quality factor $(Q)$ to the bandwidth $(\Delta \omega)$ is $.............$ s.

$A$ resistor of $50 \Omega$,an inductor of self-inductance $(\frac{2}{\pi^2}) \text{ H}$,and a capacitor of unknown capacity are connected in series to an $A$.$C$. source of $100 \text{ V}, 50 \text{ Hz}$. When the voltage and current are in phase,the value of the capacitance is: (in $\mu \text{F}$)