## MCQ (Single Correct Answer)

Given below are two statements:
Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement...

Given below are two statements:
Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first ...

As per the given graph, choose the correct representation for curve $$\mathrm{A}$$ and curve B.
Where $$\mathrm{X}_{\mathrm{C}}=$$ reactance of pure ...

Given below are two statements:
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in...

A capacitor of capacitance $$150.0 ~\mu \mathrm{F}$$ is connected to an alternating source of emf given by $$\mathrm{E}=36 \sin (120 \pi \mathrm{t}) \...

In the given circuit, rms value of current $\left(I_{\mathrm{rms}}\right)$ through the resistor $R$ is:
...

In a series LR circuit with $$\mathrm{X_L=R}$$, power factor P1. If a capacitor of capacitance C with $$\mathrm{X_C=X_L}$$ is added to the circuit the...

For the given figures, choose the correct options :
...

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator bec...

A circuit element $$\mathrm{X}$$ when connected to an a.c. supply of peak voltage $$100 \mathrm{~V}$$ gives a peak current of $$5 \mathrm{~A}$$ which ...

An alternating emf $$\mathrm{E}=440 \sin 100 \pi \mathrm{t}$$ is applied to a circuit containing an inductance of $$\frac{\sqrt{2}}{\pi} \mathrm{H}$$....

A coil of inductance 1 H and resistance $$100 \,\Omega$$ is connected to a battery of 6 V. Determine approximately :
(a) The time elapsed before the c...

A transformer operating at primary voltage $$8 \,\mathrm{kV}$$ and secondary voltage $$160 \mathrm{~V}$$ serves a load of $$80 \mathrm{~kW}$$. Assumin...

The equation of current in a purely inductive circuit is $$5 \sin \left(49\, \pi t-30^{\circ}\right)$$. If the inductance is $$30 \,\mathrm{mH}$$ then...

A direct current of $$4 \mathrm{~A}$$ and an alternating current of peak value $$4 \mathrm{~A}$$ flow through resistance of $$3\, \Omega$$ and $$2\,\O...

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

To increase the resonant frequency in series LCR circuit,

The current flowing through an ac circuit is given by
I = 5 sin(120$$\pi$$t)A
How long will the current take to reach the peak value starting from zer...

Match List-I with List-II.
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If wattless current flows in the AC circuit, then the circuit is :

Given below are two statements :
Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an ind...

A resistance of 40 $$\Omega$$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from it...

In the given circuit the AC source has $$\omega$$ = 100 rad s-1. Considering the inductor and capacitor to be ideal, what will be the current I flowin...

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 k$$\Omega$$, an inductor of inductive reactance XL = 250 $$\p...

A 100$$\Omega$$ resistance, a 0.1 $$\mu$$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate th...

A 0.07 H inductor and a 12$$\Omega$$ resistor are connected in series to a 220V, 50 Hz ac source. The approximate current in the circuit and the phase...

In a circuit consisting of a capacitance and a generator with alternating emf Eg = Eg0 sin$$\omega$$t, VC and IC are the voltage and current. Correct ...

Match List - I with List - II
List - I
List - II
(a)
$$\omega L > {1 \over {\omega C}}$$
(i)
Current ...

For a series LCR circuit with R = 100 $$\Omega$$, L = 0.5 mH and C = 0.1 pF connected across 220V$$-$$50 Hz AC supply, the phase angle between current...

AC voltage V(t) = 20 sin$$\omega$$t of frequency 50 Hz is applied to a parallel plate capacitor. The separation between the plates is 2 mm and the are...

In a series LCR circuit, the inductive reactance (XL) is 10$$\Omega$$ and the capacitive reactance (XC) is 4$$\Omega$$. The resistance (R) in the circ...

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

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

Match List - I with List - II
List - I
List - II
(a)
Phase difference between current and voltage in a purely re...

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

An AC current is given by I = I1 sin$$\omega$$t + I2 cos$$\omega$$t. A hot wire ammeter will give a reading :

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

An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to :...

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

An alternating current is given by the equation i = i1 sin $$\omega$$t + i2 cos $$\omega$$t. The rms current will be :

The angular frequency of alternating current in a L-C-R circuit is 100 rad/s. The components connected are shown in the figure. Find the value of indu...

The current (i) at time t = 0 and t = $$\infty $$ respectively for the given circuit is :...

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

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then
the time at which the energy stored in the induc...

An inductance coil has a reactance of 100 $$\Omega $$.
When an AC signal of frequency 1000 Hz is
applied to the coil, the applied voltage leads
the cu...

In LC circuit the inductance L = 40 mH and
capacitance C = 100 $$\mu $$F. If a voltage
V(t) = 10sin(314t) is applied to the circuit, the
current in th...

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 $$\Omega $$
resistor. The ratio of the currents at time...

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

Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that
passes through the battery between t = ...

A coil of self inductance 10 mH and resistance 0.1 $$\Omega $$ is connected through a switch to a battery of internal
resistance 0.9 $$\Omega $$. Afte...

A circuit connected to an ac source of emf
e = e0sin(100t) with t in seconds, gives a phase
difference of $$\pi $$/4 between the emf e and
current i. ...

In the figure shown, a circuit contains two identical resistors with resistance R = 5$$\Omega $$ and an inductance with L = 2mH. An ideal battery of 1...

A power transmission line feeds input power at 2300 V to a srep down transformer with its primary windings having 4000 turns. The output power is deli...

In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin $$\left( {30t - {\pi \over 4}} \right)$$
In one cy...

For an RLC circuit driven with voltage of amplitude vm and frequency $${\omega _0}$$ = $${1 \over {\sqrt {LC} }}$$ the current exhibits resonance. The...

An $$LCR$$ circuit is equivalent to a damped pendulum. In an $$LCR$$ circuit the capacitor is charged to $${Q_0}$$ and then connected to the $$L$$ and...

An inductor $$(L=0.03$$ $$H)$$ and a resistor $$\left( {R = 0.15\,k\Omega } \right)$$ are connected in series to a battery of $$15V$$ $$EMF$$ in a cir...

In the circuit shown here, the point $$'C'$$ is kept connected to point $$'A'$$ till the current flowing through the circuit becomes constant. Afterw...

In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $${S_1}$$ is closed, $${S_2}$$ kept open. ($$q$$ is charge on the ca...

A resistor $$'R'$$ and $$2\mu F$$ capacitor in series is connected through a switch to $$200$$ $$V$$ direct supply. Across the capacitor is a neon bul...

In the circuit shown below, the key $$K$$ is closed at $$t=0.$$ The current through the battery is
...

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...

In a series resonant $$LCR$$ circuit, the voltage across $$R$$ is $$100$$ volts and $$R = 1\,k\Omega $$ with $$C = 2\mu F.$$ The resonant frequency $$...

In an $$AC$$ generator, a coil with $$N$$ turns, all of the same area $$A$$ and total resistance $$R,$$ rotates with frequency $$\omega $$ in a magnet...

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

The phase difference between the alternating current and $$emf$$ is $${\pi \over 2}.$$ Which of the following cannot be the constituent of the circui...

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

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

The core of any transformer is laminated so as to

The power factor of $$AC$$ circuit having resistance $$(R)$$ and inductance $$(L)$$ connected in series and an angular velocity $$\omega $$ is

In a transformer, number of turns in the primary coil are $$140$$ and that in the secondary coil are $$280.$$ If current in primary coil is $$4A,$$ th...

## Numerical

In the given figure, an inductor and a resistor are connected in series with a battery of emf E volt. $$\frac{E^{a}}{2 b} \mathrm{~J} / s$$ represents...

A coil has an inductance of $$2 \mathrm{H}$$ and resistance of $$4 ~\Omega$$. A $$10 \mathrm{~V}$$ is applied across the coil. The energy stored in th...

A series combination of resistor of resistance $$100 ~\Omega$$, inductor of inductance $$1 ~\mathrm{H}$$ and capacitor of capacitance $$6.25 ~\mu \mat...

An oscillating LC circuit consists of a $$75 ~\mathrm{mH}$$ inductor and a $$1.2 ~\mu \mathrm{F}$$ capacitor. If the maximum charge to the capacitor i...

An ideal transformer with purely resistive load operates at $$12 ~\mathrm{kV}$$ on the primary side. It supplies electrical energy to a number of near...

A square shaped coil of area $$70 \mathrm{~cm}^{2}$$ having 600 turns rotates in a magnetic field of $$0.4 ~\mathrm{wbm}^{-2}$$, about an axis which i...

A series LCR circuit is connected to an ac source of $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$. The circuit contain a resistance $$\mathrm{R}=100 ~\Omega$$...

A series $\mathrm{LCR}$ circuit consists of $\mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega$, and $\mathrm{X}_{\mathrm{C}}=40 \Omega$. The i...

An inductor of $$0.5 ~\mathrm{mH}$$, a capacitor of $$20 ~\mu \mathrm{F}$$ and resistance of $$20 ~\Omega$$ are connected in series with a $$220 \math...

In an ac generator, a rectangular coil of 100 turns each having area $14 \times 10^{-2} \mathrm{~m}^{2}$ is rotated at $360 ~\mathrm{rev} / \mathrm{mi...

An inductor of inductance 2 $$\mathrm{\mu H}$$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The...

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80$$\Omega$$, an inductor of inductive reacta...

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $$\Omega$$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value o...

In the circuit shown in the figure, the ratio of the quality factor and the band width is ___________ s.
...

A capacitor of capacitance 500 $$\mu$$F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to fo...

To light, a $$50 \mathrm{~W}, 100 \mathrm{~V}$$ lamp is connected, in series with a capacitor of capacitance $$\frac{50}{\pi \sqrt{x}} \mu F$$, with $...

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...

In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is $${1 \over {K\pi }}$$ mH. T...

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...

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 im...

A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 $$\Omega$$, at resonance in the circ...

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $$\mu$$F and R = 10 $$\Omega$$ respectively. They are conn...

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of th...

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

An ac circuit has an inductor and a resistor resistance R in series, such that XL = 3R. Now, a capacitor is added in series such that XC = 2R. The rat...

The alternating current is given by $$i = \left\{ {\sqrt {42} \sin \left( {{{2\pi } \over T}t} \right) + 10} \right\}A$$The r.m.s. value of of this cu...

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 bot...

An inductor of 10 mH is connected to a 20V battery through a resistor of 10 k$$\Omega$$ and a switch. After a long time, when maximum current is set u...

A series LCR circuit of R = 5$$\Omega$$, L = 20 mH and C = 0.5 $$\mu$$F is connected across an AC supply of 250 V, having variable frequency. The powe...

In an LCR series circuit, an inductor 30 mH and a resistor 1 $$\Omega$$ are connected to an AC source of angular frequency 300 rad/s. The value of cap...

A sinusoidal voltage of peak value 250 V is applied to a series LCR circuit, in which R = 8$$\Omega$$, L = 24 mH and C = 60 $$\mu$$F. The value of pow...

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...

A transmitting station releases waves of wavelength 960 m. A capacitor of 2.56 $$\mu$$F is used in the resonant circuit. The self inductance of coil n...

A common transistor radio set requires 12 V (D.C.) for its operation. The D.C. source is constructed by using a transformer and a rectifier circuit, w...

A resonance circuit having inductance and resistance 2 $$\times$$ 10$$-$$4 H and 6.28$$\Omega$$ respectively oscillates at 10 MHz frequency. The value...