Alternating Current — JEE Main PYQs

An alternating is given by the equation $\mathrm{i}={\mathrm{i}}_1\sin \omega \mathrm{t}+{\mathrm{i}}_2\cos \omega \mathrm{t}$. Then rms current will be:

In a series LCR resonant circuit, the quality factor is measured as 100 . If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be ____ .

The alternating current is given by

The r.m.s. value of this current is ______ A

Find the peak current and resonant frequency of the following circuit (as shown in figure).

In an ac circuit, an inductor, a capacitor and a resistor are connected in series with $X_L=R=X_C$. Impedance of this circuit is:

At very high frequencies, the effective impendance of the given circuit will be ______ $\Omega$.

A 0.07 H inductor and a $12\Omega$ resistor are connected in series to a $220\mathrm{V}$, $50\mathrm{Hz}$ ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as $\frac{22}{7}$]

An AC current is given by $I=I_1\sin \omega t+I_2\cos \omega t$. A hot wire ammeter will give a reading:

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

Two circuits are shown in the figure (a) & (b). At a frequency of _____ rad/s the average power dissipated in one cycle will be same in both the circuits.

A $100\Omega$ resistance, a $0.1\mu \mathrm{F}$ capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value if inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which $\mathrm{R}=8\Omega ,\mathrm{L}=24\mathrm{mH}$ and $\mathrm{C}=60\mu \mathrm{F}$. The value of power dissipated at resonant condition is ' x ' kW . The value of x to the nearest integer …

For the given circuit, comment on the type of transformer used.

In a series LCR circuit, the inductive reactance ( ${\mathrm{X}}_{\mathrm{L}}$ ) is $10\Omega$, and the capacitive reactance ( ${\mathrm{X}}_{\mathrm{C}}$ ) is $4\Omega$. The resistance (R) in the circuit is $6\Omega$. The power factor of the circuit is :

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved?

In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

An AC source rated $220\mathrm{V},50\mathrm{Hz}$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

A $750\mathrm{Hz},20\mathrm{V}$ (rms) source is connected to a resistance of $100\Omega$ an inductance of 0.1803 H and a capacitance of $10\mu \mathrm{F}$ all in series. The time in which the resistance (heat capacity $2\mathrm{J}/{}^{\circ }\mathrm{C}$) will get heat …

In a series LR circuit, power of 400 W is dissipated from a source of $250\mathrm{V},50\mathrm{Hz}$. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as …

An AC circuit has $\mathrm{R}=100\Omega ,\mathrm{C}=2\mu \mathrm{F}$ and $\mathrm{L}=80\mathrm{mH}$, connected in series. The quality factor of the circuit is:

An alternating voltage $\mathrm{v}(\mathrm{t})=220\sin 100\pi \mathrm{t}$ 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 circuit connected to an ac source of emf $e=e_0\sin (1000t)$ with t in seconds, gives a phase difference of $\frac{\pi }{4}$ between the emf e and current i. Which of the following circuits will exhibit this?

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5 A and its efficiency is $90\%$, the outp …

A series AC circuit containing an inductor ( 20 mH ), a capacitor ( $120\mu \mathrm{F}$ ) and a resistor ( $60\Omega$ ) is driven by an AC source of $24\mathrm{V}/50\mathrm{Hz}$. The energy dissipated in the circuit in 60 s is:

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coils is 10 A, then the input voltage and current in the primary coil are:

For an RLC circuit driven with voltage of amplitude $v_{\mathrm{m}}$ and frequency ${\omega }_{\mathrm{o}}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exibits resonance. The quality factor, Q is given by :

In an a.c. circuit, the instantaneous e.m.f. and current are given by


In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively :

An arc lamp requires a direct current of 10 A and 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :

In a series LCR circuit R = $200\Omega$ and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$. On taking out the inductor from the circuit the c …

In an a.c. circuit the voltage applied is $E=E_0\sin \omega t$. The resulting current in the circuit is $I=I_0\sin \left(\omega t-\frac{\pi }{2}\right)$. The power consumption in the circuit is given by

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

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of

A circuit has a resistance of $12\Omega$ and an impedance of $15\Omega$. The power factor of the circuit will be

The phase difference between the alternating current and emf is $\pi /2$. Which of the following cannot be the constituent of the circuit?

Alternating current can not be measured by D.C. ammeter because

In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be

In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to