Alternating Current

An AC voltage \(V=20 \sin 200 \pi t\) is applied to a series LCR circuit which drives a current \(I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)\). The average power dissipated is:

In a series LCR circuit, the maximum amplitude of current is \({I}_{0}\) when the resistance is \(R\). What will be the maximum amplitude of current if the resistor is replaced by a resistor of resistance \(R\mathrm{/}2\)?

(Shift II Memory Based)

An a.c. source of angular frequency \(\omega\) is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to \(\omega /4\), (keeping the voltage unchanged) the current is found to be I/3. The ratio of resistance to reactance at frequency \(\omega\) is

[JEE Main 2026, 5 Apr (Shift 1)]

Primary side of a transformer is connected to \(230\ V , 50 \ Hz\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46 \ \Omega\). The power consumed in it is :

[JEE Main 2024, 27 Jan (Shift 2)]

Primary side of a transformer is connected to \(230\ V , 50 \ Hz\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46 \ \Omega\). The power consumed in it is :

[JEE Main 2024, 27 Jan (Shift 2)]

\text { If } I=I_A \sin \omega t+I_B \cos \omega t \text {, then find } r m s \text { value of current. }

(Shift I - Memory Based)

An alternating current is given by \(I={I}_{A}\sin \omega t+{I}_{B}\cos \omega t\). The r.m.s current will be:

[JEE Main 2025, 24 Jan (Shift 1)]

\text { If } I=I_A \sin \omega t+I_B \cos \omega t \text {, then find } r m s \text { value of current. }

(Shift I - Memory Based)

An alternating voltage \(V(t)=220 \sin 100 \pi t\) volt is applied to a purely resistive load of \(50 \Omega\). The time taken for the current to rise from half of the peak value to the peak value is:

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is \(I_0\). If the value of resistance \(R\) becomes twice of its initial value then amplitude of current at resonance will be

[JEE Main 2025, 22 Jan (Shift 2)]

In a series LCR circuit, inductance L = 10 mH and capacitance C = 10 nF. The angular frequency of the source when current has maximum amplitude in the circuit is

(Shift - II Memory Based)

An alternating current is represented by the equation, \(\mathrm{i}=100\sqrt{2}\sin (100\mathrm{πt})\) ampere. The RMS value of current and the frequency of the given alternating current are:

[JEE Main 2025, 4 Apr (Shift 1)]

An AC voltage \(V=20 \sin 200 \pi t\) is applied to a series LCR circuit which drives a current \(I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)\). The average power dissipated is:

[JEE Main 2024, 31 Jan (Shift 2)]

A series L.R circuit connected with an ac source \(E=(25\sin 1000t)V\) has a power factor of\(\frac{1}{\sqrt{2}}\). If the source of emf is changed to

E =\((20\sin 2000\mathrm{t})\mathrm{V}\), the new power factor of the circuit will be :

In a series LCR circuit, inductance L = 10 mH and capacitance C = 10 nF. The angular frequency of the source when current has maximum amplitude in the circuit is

(Shift - II Memory Based)

A LCR series circuit driven with, \({E}_{rms}=90V\) at frequency \({f}_{d}=30\) Hz has resistance \(R=80\Omega\), an inductance with inductive reactance \({X}_{L}=20.0\Omega\) and capacitance with capacitive reactance \({X}_{C}=80.0\Omega\). The power factor of the circuit is _____ .

[JEE Main 2026, 6 Apr (Shift 1)]

An alternating voltage \(V(t)=220 \sin 100 \pi t\) volt is applied to a purely resistive load of \(50 \ \Omega\). The time taken for the current to rise from half of the peak value to the peak value is:

[JEE Main 2024, 30 Jan (Shift 2)]

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is \(I_0\). If the value of resistance \(R\) becomes twice of its initial value then amplitude of current at resonance will be

An electric bulb rated as 100 W-220 V is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :

[JEE Main 2025, 3 Apr (Shift 2)]

An alternating current is given by \(I={I}_{A}\sin \omega t+{I}_{B}\cos \omega t\). The r.m.s current will be

[JEE Main 2025, 24 Jan (Shift 1)]

In a series LCR circuit, the maximum amplitude of current is \({I}_{0}\) when the resistance is \(R\). What will be the maximum amplitude of current if the resistor is replaced by a resistor of resistance \(R\mathrm{/}2\)?

(Shift II Memory Based)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R/\sqrt{{R}^{2}+{\omega }^{2}{L}^{2}}\right)\), where \(\omega\) is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below:

Match the List-I with List-II.

Choose the correct answer from the options given below: [JEE Main 2023, 1 Feb (Shift 1)]

An alternating voltage \(V=V_0 \sin \omega t\) is applied across a circuit. As a result, a current \(I=I_0 \sin \left(\omega t-\frac{\pi}{2}\right)\) flows in it. The power consumed per cycle is

An alternative voltage V = 260 sin (628t) is connected across a pure inductor of 5mH. Inductive reactance in the circuit is:

[JEE Main 2023, 31 Jan (Shift 2)]

An LCR circuit contains resistance of \(110\Omega\) and a supply of \(220\mathrm{V}\) at \(300\mathrm{rad}/s\) angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by \(45^\circ\). If on the other hand, only inductor is removed the current leads by \(45^\circ\) with the applied voltage. The rms current flowing in the circuit will be:

[JEE Main 2021, 25 Feb (Shift 2)]

Given below are two statements:
Statement-I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs

Statement-II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below :

[JEE Main 2023, 10 Apr (Shift 1)]

A capacitor of capacitance \(150.0\mu \mathrm{F}\) is connected to an alternating source of emf given by\(E=36\sin (120\pi t)\) V. The maximum value of current in the circuit is approximately equal to:

[JEE Main 2023, 6 Apr (Shift 2)]

In an LC oscillator, if the values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of the oscillator becomes x times its initial resonant frequency\({\omega }_{0}\). The value of x is:

[JEE Main 2023, 25 Jan (Shift 1)]

Given below are two statements:
Statement-I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement-II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its nonzero power factor.

In the light of above statements, choose the correct answer from the options given below :

In a circuit, a metal filament lamp is connected in series with a capacitor of capacitance \(\mathrm{C} \mu \mathrm{F}\) across a \(200 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power consumed by the lamp is \(500 \mathrm{~W}\) while the voltage drop across it is \(100 \mathrm{~V}\). Assume that there is no inductive load in the circuit. Take rms values of the voltages. The magnitude of the phase angle (in degrees) between the current and the supply voltage is \(\varphi\). Assume, \(\pi \sqrt{3} \approx 5\). The value of C is ...........μF

Match the List-I with List-II.

Choose the correct answer from the options given below:

A series LCR circuit driven by \(300\mathrm{V}\) at a frequency of \(50\mathrm{Hz}\) contains a resistance \(\mathrm{R}=3\mathrm{kΩ}\), an inductor of inductive reactance \({X}_{L}=250\pi \Omega\) and an unknown capacitor. The value of capacitance to maximize the average power should be: Take \(\left.({\pi }^{2}=10\right)\)

[JEE Main 2021, 26 Aug (Shift 1)]

A 100 \(\Omega\) resistance, a \(0.1\mu F\) capacitor and an inductor are connected in series across a \(250\mathrm{V}\) supply at variable frequency. Calculate the value of inductance of the inductor at which resonance will occur. Given that the resonant frequency is \(60\mathrm{Hz}\).[JEE Main 2021, 27 Jul (Shift 2)]

An alternating voltage source \(\mathrm{V}=260\sin (628t)\) is connected across a pure inductor of \(5\mathrm{mH}\). Inductive reactance in the circuit is:

[JEE Main 2023, 31 Jan (Shift 2)]

Given below are two statements:
Statement-I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs

Statement-II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statements, choose the correct answer from the options given below :

\(\mathrm{A}10\Omega\) resistance is connected across \(220\mathrm{V}-50\mathrm{Hz}\mathrm{AC}\) supply. The time taken by the current to change from its maximum value to the rms value is:

[JEE Main 2021, 25 Jul (Shift 2)]

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes x times its initial resonant frequency \(\omega\)₀. The value of x is:

[JEE Main 2023, 25 Jan (Shift 1)]

An alternating current is given by the equation \(i={i}_{1}\sin \omega t+{i}_{2}\)\(\cos \omega t\). Then rms current will be:

[JEE Main 2021, 26 Feb (Shift 1)]