Alternating Current

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be ______.

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/°C will get heated by 16°C is ______ s.

A telegraph line of length 100 km has a capacity of 0.01 $\mu$F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ______ mH. (if $\pi=\sqrt{10}$)

In the given circuit, the magnitude of $V_L$ and $V_C$ are twice that of $V_R$. Given that $f=50$ Hz, the inductance of the coil is $\dfrac1{K\pi}$ mH. The value of K is ______.

For a series LCR circuit, I vs $\omega$ curve is shown :

(a) To the left of $\omega_r$, the circuit is mainly capacitive.

(b) To the left of $\omega_r$, the circuit is mainly inductive.

(c) At $\omega_r$, impedance of the circuit is equal to the resistance of the circuit.

(d) At $\omega_r$, impedance of the circuit is 0.

Choose the most appropriate answer from the options given below :

An inductor of 0.5 mH, a capacitor of 200 $\mu$F and a resistor of 2 $\Omega$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ $\times10^2$ Hz.

In series RLC resonator, if the self inductance and capacitance become double, the new resonant frequency ($f_2$) and new quality factor ($Q_2$) will be :

($f_1$ = original resonant frequency, $Q_1$ = original quality factor)

A series LCR circuit with $R=\dfrac{250}{11}$ $\Omega$ and $X_L=\dfrac{70}{11}$ $\Omega$ is connected across a 220 V, 50 Hz supply. The value of capacitance needed to maximize the average power of the circuit will be ______ $\mu$F. (Take : $\pi=\dfrac{22}7$)

To increase the resonant frequency in series LCR circuit,

The rms value of conduction current in a parallel plate capacitor is 6.9 $\mu$A. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

In a series LR circuit $X_L=R$ and power factor of the circuit is $P_1$. When capacitor with capacitance C such that $X_L=X_C$ is put in series, the power factor becomes $P_2$. The ratio $\dfrac{P_1}{P_2}$ is :

The effective current I in the given circuit at very high frequencies will be ______ A.

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :

To light, a 50 W, 100 V lamp is connected, in series with a capacitor of capacitance $\dfrac{50}{\pi\sqrt x}$ μF, with 200 V, 50 Hz AC source. The value of $x$ will be ______.

A series LCR circuit has L = 0.01 H, R = 10 Ω and C = 1 μF and it is connected to ac voltage of amplitude $(V_m)$ 50 V. At frequency 60% lower than resonant frequency, the amplitude of current will be approximately :

The equation of current in a purely inductive circuit is $5\sin(49\pi t-30^\circ)$. If the inductance is 30 mH then the equation for the voltage across the inductor, will be :

$\left\{\text{Let }\pi=\dfrac{22}7\right\}$

The frequencies at which the current amplitude in an LCR series circuit becomes $\dfrac1{\sqrt2}$ times its maximum value, are 212 rad s$^{-1}$ and 232 rad s$^{-1}$. The value of resistance in the circuit is R = 5 Ω. The self inductance in the circuit is ______ mH.

A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be