In an $L-C-R$ series circuit,the value of only capacitance $C$ is varied. The resulting variation of resonance frequency $f_0$ as a function of $C$ can be represented as

An $LC$ circuit consists of a capacitor and a coil with a large number of turns. Suppose all the linear dimensions of all elements of the circuit are increased by a factor of $2$ while keeping the number of turns on the coil constant. How much does the resonant frequency of the circuit change?

$A$ series $LCR$ circuit with $R = 20 \ \Omega$, $L = 1.6 \ \text{H}$ and $C = 40 \ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is . . . . . . $\Omega$.

In an $LCR$ circuit,the inductance is changed from $L$ to $9 L$. For the same resonant frequency,the capacitance should be changed from $C$ to:

In an $LCR$ series circuit at resonance:

$A$ circuit containing resistance $R_1$,inductance $L_1$,and capacitance $C_1$ connected in series resonates at the same frequency $f_r$ as another circuit containing $R_2$,$L_2$,and $C_2$ in series. If the two circuits are connected in series,then the new frequency at resonance is