The motor of an electric fan has a self inductance of 10 H, and is connected to a 50-Hz ac supply in series with a capacitor. If maximum power transfer occurs when $X_L=X_{C}X\_L\; =\; X\_C$ , the capacitance of the capacitor is

The reactance of a coil is 157 $\mathrm{\Omega }\backslash Omega$. On connecting the coil across a source of frequency 100 Hz, the current lags behind the emf by 45°. The inductance of the coil is

In a series LCR circuit, the power factor at resonance is

The current in an LC circuit at resonance is called

In a series LCR circuit at resonance, the applied emf and current are

In a series LCR circuit, $R=3\mathrm{\Omega },X_L=8\mathrm{\Omega }and{X}_C=4\mathrm{\Omega }R\; =\; 3\; \backslash Omega,\; X\_L\; =\; 8\; \backslash Omega\; \backslash \; and\; \backslash \; X\_C\; =\; 4\; \backslash Omega$. The impedance of the circuit is

A sinusoidal emf of peak value $150\sqrt{2}V150\; \backslash sqrt\; 2\; \backslash \; V$ is applied to a series LCR circuit in which R = 3 $\mathrm{\Omega }\backslash Omega$ and Z = 5 $\mathrm{\Omega }\backslash Omega$. The rms current in the circuit is

In a series LCR circuit, $R=3\mathrm{\Omega },Z=5\mathrm{\Omega },i_{rms}=40AR\; =\; 3\; \backslash Omega,\; Z\; =\; 5\; \backslash Omega,\; i\_\{rms\}\; =\; 40\; A$ and power factor = 0.6. The average power dissipated in the circuit is

A parallel LC resonant circuit is used as

A senes LCR resonant circuit is used as