In the given circuit,the voltmeter reads $75 \ V$. The value of $C$ is $.... \mu F$. (Given: $\pi^2 = 10$)

An a.c. e.m.f. of peak value $V_0 = 230 \ V$ and frequency $f = 50 \ Hz$ is connected to a circuit with $R = 11.5 \ \Omega$,$L = 2.5 \ H$ and a capacitor $C$ all in series. For the current in the circuit to be maximum,the circuit must be in resonance. Find the value of $C$ and the maximum current $I_{max}$ (take $\pi^2 = 10$).

The figure shows a series $LCR$ circuit connected to a variable frequency $230 \; V$ source. Given $L = 5.0 \; H$,$C = 80 \; \mu F$,and $R = 40 \; \Omega$.
$(a)$ Determine the source frequency which drives the circuit in resonance.
$(b)$ Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
$(c)$ Determine the $rms$ potential drops across the three elements of the circuit. Show that the potential drop across the $LC$ combination is zero at the resonating frequency.

In a series $LCR$ resonant circuit,the capacitance is changed from $C$ to $3C$. To obtain the same resonant frequency,the inductance should be changed from $L$ to

Explain resonance for an $L-C-R$ series circuit and write its uses. In what kind of circuit will it be possible?

The $Q$ factor of a series $LCR$ circuit with $L = 2 \ H$,$C = 32 \ \mu F$,and $R = 10 \ \Omega$ is: