Alternating Current

When an inductance '$L$' and resistor '$R$' are connected in series to $25$V, $50$ Hz supply, a current of $0.5$ A flows in the circuit. The current lags behind in phase from applied voltage by $\left(\dfrac{\pi}{3}\right)$ radian. The valu...

Which graph shows the correct variation of r.m.s. current '$i$' with frequency '$f$' of a.c. in case of series resonant circuit ?

In a series LCR circuit, the voltage across R is $100$ V, $R = 1\,\text{K}\,\Omega$ and $C = 2\,\mu\text{F}$. The angular frequency $\omega$ is $200$ rad s$^{-1}$. At resonance, the voltage across '$L$' is

A current of 4 A is flowing at 230 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 2300 V and 40 % of power is lost, then the current in the secondary will be

In a L-R circuit of 4 mH inductance and $3\ \Omega$ resistance, e.m.f. $E = \cos(1000t)$ V is applied. The amplitude of current is

Given below are the two circuits, choose the correct option.

In an LCR series circuit an alternating voltage source of frequency $F$ is connected. The current leads the voltage by $45^\circ$. The value of $L$ is

In an LCR circuit at resonance, the a.c. source current isA) maximum in a series LCR circuit only.B) maximum in a parallel LCR circuit only.C) maximum in both series and parallel LCR circuits.D) minimum in both series and parallel LCR circu...

An alternating voltage $e = 150\sqrt{2}\sin 100t$ volt is applied to a capacitor of capacity $2\ \mu\text{F}$. The root mean square value of current in the circuit is

For a series LCR circuit inductive reactance $X_L$ is equal to resistance $R$ and also equal to twice the capacitive reactance $X_C$. The impedance of the circuit and the phase difference between voltage V and current i are respectively

In series LCR circuit $R = 10\,\Omega$ and impedance is $30\,\Omega$. An r.m.s. voltage $210$ V, is applied across the circuit. The true power consumed in AC circuit is

When a.c. source is connected across a pure capacitor, the correct phase relation between current and emf is shown in figure.

Two coils P and S have a mutual inductance of ($\pi$) mH. The secondary coil S has resistance $4\,\Omega$ and self inductance $(60/\pi)$ mH. If the current in the primary is $I_p = 12\sin(50\pi t)$, then the maximum value of the current ind...

In an oscillating LC circuit the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor (q) is

In an a.c. circuit, a resistance R is connected in series with an inductance 'L'. If phase angle between voltage and current is $45^\circ$, the value of inductive reactance will be($\sin 45^\circ = \dfrac{1}{\sqrt{2}} = \cos 45^\circ$)

An a.c. source is applied to a series LR circuit with $X_L = 3R$ and power factor is $X_1$. Now a capacitor with $X_c = R$ is added in series to LR circuit and power factor is $X_2$. The ratio $X_1$ to $X_2$ is

In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

In an LCR series circuit, the potential difference across the terminals of the inductor, capacitor and resistor is 60 V, 30 V and 40 V respectively. Then supply voltage will be equal to

In the series LCR circuit shown in figure the impedance is

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$\omega$'. Keeping the voltage same, if the frequency is changed to $\left(\dfrac{\omega}{3}\right)$ the current becomes half of the...

A transformer has 120 turns in the primary coil and carries 5A current. Input power is one kilowatt. To have 560 V output, the number of turns in secondary coil will be

In LCR series circuit at resonance

The LC series resonant circuit produces a resonant frequency '$f$'. If L is tripled and 'C' is increased by 3C, the resonant frequency will be

The resistor '$R$' inductance '$L$' and capacitance '$C$' are connected in series with an a.c. source. When 'L' is removed from the circuit, the phase difference between voltage and current in the circuit is $\dfrac{\pi}{3}$. If instead, C ...

In a series LCR circuit alternating e.m.f. and current are given by the equations $V = V_0\sin(\omega t)$ and $I = I_0\sin\left(\omega t + \dfrac{\pi}{3}\right)$ respectively. The average power dissipated in the circuit over one cycle of a....

In an a.c. circuit with pure capacitance 'C' and a.c. source $E = E_0\sin\omega t$, the equation of instantaneous current is given by

In LCR circuit, at a particular angular frequency the capacitive reactance and inductive reactance is same. If the angular frequency is doubled, the ratio of the reactance of the capacitor to that of the inductor will be

A step down transformer has turns ratio 20:1. If 8V are applied across $0.4\ \Omega$ secondary then the primary current will be

An alternating e.m.f. is given by $e = e_0 \sin\omega t$. In what time the e.m.f. will have half its maximum value, if 'e' Starts from zero?

With gradual increase in frequency of an a.c. supply, the impedance of an LCR series circuit

When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit

An inductor of inductance $2\ \mu\text{H}$ is connected in series with a resistance, a variable capacitor and an a.c. source of 10 kHz. The value of capacitance for which maximum current is drawn in to the circuit is $\dfrac{1}{x}\ \text{F}...

Series LCR circuit containing an a.c. source of 100V has a inductor and a capacitor of reactance $24\ \Omega$ and $16\ \Omega$ respectively. If a resistance of $6\ \Omega$ is connected in series, then the potential difference across the ser...

Alternating current of peak value $\left(\dfrac{2}{\pi}\right)$ A flows through the primary coil of a transformer. The coefficient of mutual inductance between primary and secondary coils is 1H. The peak value of induced e.m.f. in the secon...

A coil has inductive reactance $3$ H. The ratio of its reactance when it is first connected to an a.c. source and then to d.c. source is

Determine the frequency for which a $10\,\mu\text{F}$ capacitor has a reactance of $2 \times 10^{-3}\,\Omega$.

A series LCR circuit is connected to an a.c. source of $220$ V, $50$ Hz. The circuit contains a resistance $R = 80\,\Omega$, an inductor of inductive reactance $70\,\Omega$ and capacitor of capacitive reactance $130\,\Omega$. The power fact...

In an LCR series circuit, at resonance,

A series resonant circuit consists of an inductor 'L' and capacitor 'C' which produces resonant frequency 'f'. If 'L' is increased by '2L' and 'C' is changed to '9C' the resonant frequency will be

An electric lamp connected in series with a capacitor and an a.c source is glowing with certain brightness. On reducing the frequency of source the brightness of the lamp

A resistor of 100 $\Omega$, inductor of self inductance $\left(\dfrac{4}{\pi^2}\right)$ H and a capacitor of unknown capacity are connected in series to an a.c. source of 200 V and 50 Hz. When the current and voltage are in phase, the value...

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In what time the e.m.f. will have half its maximum value, if 'e' starts from zero? ($\sin 30^\circ = 0.5$)

In series LCR resonant circuit, R=800 $\Omega$, C = 2 $\mu$F and voltage across resistance is 200 V. The angular frequency is 250 rad/s. At resonance the voltage across the capacitance is

In series LCR circuit C = 2 uF, L=1 mH and R= 10 $\Omega$. What is the ratio of energies stored in the capacitor and inductor when maximum current flows through circuit?

In a series LR circuit with $X_L = R$. Power factor is $P_1$. If a capacitor of capacitance $C$ with $X_c = X_L$ is added to the circuit the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be :

An inductor of $0.5$ mH, a capacitor of $20$ $\mu$F and resistance $20\,\Omega$ are connected in series with a $220$ V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2}$ A. The value o...

In the circuit shown, the ratio of the quality factor and the band width is(Given: band width = R/L)

In the circuit shown below, the ac source has voltage $V = 30 \cos(\omega t)$ volt with $\omega = 2000$ rad/s. What will be the amplitude of the current?

In an AC circuit $E = 50 \sin(500 t)$, $I = 600 \sin\left(500 t + \dfrac{\pi}{3}\right) mA$. What is the power dissipated in the circuit? [$\cos 60^\circ = 0.5$]

An inductor of reactance $100$ $\Omega$, a capacitor of reactance $50$ $\Omega$, and a resistor of resistance $50$ $\Omega$ are connected in series with an AC source of $10$ V, $50$ Hz. Average power dissipated by the circuit is ____