In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad/s$. At resonance,the voltage across $L$ is......$V$.

$L=2 \text{ H}, C=5 \text{ mF}$ and $R=12 \text{ } \Omega$ are connected in series to an a.c. generator of frequency $50 \text{ Hz}$. Then:

$A$ series $LCR$ circuit with $R=20\; \Omega, L=1.5\; H$ and $C=35\; \mu F$ is connected to a variable-frequency $200\; V$ $ac$ supply. When the frequency of the supply equals the natural frequency of the circuit,what is the average power (in $W$) transferred to the circuit in one complete cycle?

The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by:

In a series $L-C-R$ circuit,the capacitance is changed from $C$ to $2C$. To obtain the same resonance frequency,the inductance should be changed from $L$ to:

In a series $LCR$ circuit,at resonance,the peak value of current will be [where $E_0$ is peak emf,$R$ is resistance,$\omega L$ is inductive reactance,and $1/\omega C$ is capacitive reactance].