Electromagnetic Induction & AC · JEE Main previous year questions

1. A.
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4. D.

In an LCR series circuit, an inductor $30\text{ mH}$ and a resistor $1\Omega$ are connected to an AC source of angular frequency $300\text{ rad/s}$. The value of capacitance for which, the current leads the voltage by $45^{\circ }$ is $\frac{1}{x}\times 10^{-3}\text{ F}$. Then the value of x is ________.

In a series LCR circuit, the inductive reactance ($X_L$) is $10\Omega$ and the capacitive reactance ($X_C$) is $4\Omega$. The resistance (R) in the circuit is $6\Omega$. The power factor of the circuit is :

1. A.$\frac{1}{2}$
2. B.$\frac{\sqrt{3}}{2}$
3. C.$\frac{1}{\sqrt{2}}$
4. D.$\frac{1}{2\sqrt{2}}$

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 is _________.

An alternating current is given by the equation $i=i_1\sin \omega t+i_2\cos \omega t$. The rms current will be :

1. A.$\frac{1}{\sqrt{2}}{\left(i_1^2+i_2^2\right)}^{\frac{1}{2}}$
2. B.$\frac{1}{\sqrt{2}}(i_1+i_2)$
3. C.$\frac{1}{\sqrt{2}}(i_1+i_2{)}^2$
4. D.$\frac{1}{2}{\left(i_1^2+i_2^2\right)}^{\frac{1}{2}}$

An LCR circuit contains resistance of $110\Omega$ and a supply of 220 V at 300 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 :

1. A.1 A
2. B.2.5 A
3. C.2 A
4. D.1.5 A

Match List I with List II. | | List I | | List II | | :--- | :--- | :--- | :--- | | (a) | Rectifier | (i) | Used either for stepping up or stepping down the a.c. voltage | | (b) | Stabilizer | (ii) | Used to convert a.c. voltage into d.c. voltage | | (c) | Transformer | (iii) | Used to remove any ripple in the rectified output voltage | | (d) | Filter | (iv) | Used for constant output voltage even when the input voltage or load current change | Choose the correct answer from the options given below :

1. A.(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)
2. B.(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
3. C.(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
4. D.(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

1. A.T : Large retentivity, small coercivity
2. B.P : Large retentivity, large coercivity
3. C.P : Small retentivity, large coercivity
4. D.T : Large retentivity, large coercivity

An inductance coil has an impedance of $100\Omega$. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by $45^{\circ }$. The self-inductance of the coil is

1. A.$6.7\times 10^{-7}\mathrm{H}$
2. B.$1.1\times 10^{-1}\mathrm{H}$
3. C.$5.5\times 10^{-5}\mathrm{H}$
4. D.$1.1\times 10^{-2}\mathrm{H}$

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ________.

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 coil is 10A, then the input voltage and current in the primary coil are :

1. A.220 V and 20 A
2. B.220 V and 10A
3. C.440 V and 5A
4. D.440 V and 20 A

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the transformer is 5 A, and its efficiency is 90%, the output current would be ;

1. A.50 A
2. B.45 A
3. C.25 A
4. D.20 A

A sinusoidal voltage of peak value 283 V and angular frequency 320/s is applied to a series LCR circuit. Given that R=$5\Omega$, L=25 mH and C=1000 $\mu \mathrm{F}$. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

1. A.$10\Omega \text{and}{\tan }^{-1}\left(\frac{5}{3}\right)$
2. B.$7\Omega \text{and}45^{\circ }$
3. C.$10\Omega \text{and}{\tan }^{-1}\left(\frac{8}{3}\right)$
4. D.$7\Omega \text{and}{\tan }^{-1}\left(\frac{5}{3}\right)$

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current $\mathrm{I}={\mathrm{I}}_o\cos (\omega t)$. The emf induced in the smaller inner loop is nearly :

1. A.$\frac{\pi {\mu }_o{\mathrm{I}}_o}{2}\cdot \frac{a^2}{b}\omega \sin (\omega t)$
2. B.$\frac{\pi {\mu }_o{\mathrm{I}}_o}{2}\cdot \frac{a^2}{b}\omega \cos (\omega t)$
3. C.$\pi {\mu }_o{\mathrm{I}}_o\frac{a^2}{b}\omega \sin (\omega t)$
4. D.$\frac{\pi {\mu }_o{\mathrm{I}}_o{b}^2}{a}\omega \cos (\omega t)$

An arc lamp requires a direct current of 10 A at 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 :

1. A.0.044 H
2. B.0.065 H
3. C.80 H
4. D.0.08 H

1. A.$A$ for transformers and $B$ for electric generators.
2. B.$B$ for electromagnets and transformers.
3. C.$A$ for electric generators and transformers.
4. D.$A$ for electromagnets and $B$ for electric generators.

1. A.
2. B.
3. C.
4. D.

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 $200rad/s$. At resonance the voltage across $L$ is

1. A.$2.5\times 10^{-2}\mathrm{V}$
2. B.$40\mathrm{V}$
3. C.$250\mathrm{V}$
4. D.$4\times 10^{-3}\mathrm{V}$

Two concentric coils each of radius equal to $2\pi \mathrm{cm}$ are placed at right angles to each other. $3$ ampere and $4$ ampere are the currents flowing in each coil respectively . The magnetic induction in $Weber/{\mathrm{m}}^2$ at the center of the coils will be $(\mu =4\pi \times 10^{-7}Wb/A.m)$

1. A.$10^{-5}$
2. B.$12\times 10^{-5}$
3. C.$7\times 10^{-5}$
4. D.$5\times 10^{-5}$

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

1. A.$R,L$
2. B.$C\text{ alone}$
3. C.$L\text{ alone}$
4. D.$L,C$

A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

1. A.$\frac{{\mu }_0}{4\pi },\frac{2i}{r}$ tesla
2. B.zero
3. C.infinite
4. D.$\frac{2i}{r}$ tesla

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

1. A.Average value of current for complete cycle is zero
2. B.$A.C.$ Changes direction
3. C.$A.C.$ can not pass through $D.C.$ Ammeter
4. D.$D.C.$ Ammeter will get damaged.

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

1. A.$L/2$
2. B.$2L$
3. C.$4L$
4. D.$L/4$

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 $4\mathrm{A}$, then that in the secondary coil is

1. A.$4\mathrm{A}$
2. B.$2\mathrm{A}$
3. C.$6\mathrm{A}$
4. D.$10\mathrm{A}$

1. A.$3.66\mathrm{H}$
2. B.$9\mathrm{H}$
3. C.$0.66\mathrm{H}$
4. D.$1\mathrm{H}$