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Arihant AIEEE Physics

D.B. Singh

Chapter 30

Alternating Current and Electromagnetic Woves - all with Video Answers

Educators

Chapter Questions

03:19

Problem 1

An A.C. source of voltage $V=100 \sin 100 \pi t$ is connected to a resistor of resistance $20 \Omega$. The rms value of current through resistor is :
(a) $10 \mathrm{~A}$
(b) $\frac{10}{\sqrt{2}} \mathrm{~A}$
(c) $\frac{5}{\sqrt{2}} \mathrm{~A}$
(d) none of these

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01:40

Problem 2

In previous problem, average value of current for long time is :
(a) zero
(b) $\frac{5}{\sqrt{2}} \mathrm{~A}$
(c) $10 \mathrm{~A}$
(d) none of these

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01:28

Problem 3

In previous problem, the average value for half cycle is :
(a) $\frac{10}{\pi} \mathrm{A}$
(b) $\frac{5}{\pi} \mathrm{A}$
(c) zero
(d) none of these

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01:33

Problem 4

In previous problem, total charge transferred through resistor in long time is:
(a) zero
(b) $\frac{2 I_{0}}{\pi}$
(c) $\frac{I_{0}}{25 \pi}$
(d) none of these

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01:47

Problem 5

In previous problem, total charge transferred in $1 / 100$ second is :
(a) $1 / 10 \pi C$
(b) $1 / 5 \pi \mathrm{C}$
(c) zero
(d) none of these

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02:16

Problem 6

In previous problem, total heat generated in one cycle is :
(a) $\sqrt{2} \mathrm{~J}$
(b) $5 \mathrm{~J}$
(c) $4 \sqrt{2} \mathrm{~J}$
(d) zero

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01:32

Problem 7

In previous problem, power factor is :
(a) 1
(b) 0
(c) $1 / 2$
(d) none of these

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02:04

Problem 8

The peak and rms value of current in A.C. circuit. The current is represented by the equation $i=5 \sin \left(300 t-\frac{\pi}{4}\right)$. where $t$ is in seconds, and ' $i^{\prime}$ in ampere :
(a) $5 \mathrm{~A}, 3.535 \mathrm{~A}$
(b) $5 \mathrm{~A}, 5.53 \mathrm{~A}$
(c) $3 \mathrm{~A}, 3.53 \mathrm{~A}$
(d) $6.25 \mathrm{~A}, 5.33 \mathrm{~A}$

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02:42

Problem 9

An A.C. voltage is represented by $e=220 \sqrt{2} \cos (50 \pi) t$
How many times will the current become zero in one sec?
(a) 50 times
(b) 100 times
(c) 30 times
(d) 25 times

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02:15

Problem 10

The average value for half cycle in a $200 \mathrm{~V}$ A.C. source is :
(a) $180 \mathrm{~V}$
(b) $200 \mathrm{~V}$
(c) $220 \mathrm{~V}$
(d) none of these

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02:27

Problem 11

Two alternating currents are given by
$$
\begin{array}{ll}
& I_{1}=I_{0} \sin \omega t \\
\text { and } & I_{2}=I_{0} \cos (\omega t+\phi)
\end{array}
$$
The ratio of rms values is :
(a) $1: 1$
(b) $1: \phi$
(c) $1: 2$
(d) none of these

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02:51

Problem 12

A current $I=3+8 \sin 100 t$ is passing through a resistor of resistance $10 \Omega$. The effective value of current is :
(a) $5 \mathrm{~A}$
(b) $10 \mathrm{~A}$
(c) $4 \sqrt{2} \mathrm{~A}$
(d) $3 / \sqrt{2} \mathrm{~A}$

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02:58

Problem 13

An alternating voltage $V=30 \sin 50 t+40 \cos 50 t$ is applied to a resistor of resistance $10 \Omega$. The rms value of current through resistor is :
(a) $\frac{5}{\sqrt{2}} \mathrm{~A}$
(b) $\frac{10}{\sqrt{2}} \mathrm{~A}$
(c) $\frac{7}{\sqrt{2}} \mathrm{~A}$
(d) $7 \mathrm{~A}$

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02:23

Problem 14

The electric field in an electromagnetic wave is given by
$$
E=(100 \mathrm{~N} / \mathrm{C}) \sin \omega\left(t-\frac{x}{c}\right)
$$
If the energy contained in a cylinder of cross-section $10 \mathrm{~cm}^{2}$ and length $50 \mathrm{~cm}$ along the $x$ -axis is $4.4 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{3}$, then the intensity of the wave is:
(a) $12.4 \mathrm{~W} / \mathrm{m}^{2}$
(b) $13.2 \mathrm{~W} / \mathrm{m}^{2}$
(c) $15.7 \mathrm{~W} / \mathrm{m}^{2}$
(d) $11.9 \mathrm{~W} / \mathrm{m}^{2}$

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06:09

Problem 15

The root mean square value of voltage, if an alternating voltage is given by $e=e_{1} \sin \omega t+e_{2} \cos \omega t$ is:
(a) $\frac{\sqrt{e_{1}^{2}+e_{2}^{2}}}{2}$
(b) $\frac{\sqrt{e_{1}^{2}-e_{2}^{2}}}{2}$
(c) $\sqrt{e_{1} e_{2}}$
(d) none of these

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05:03

Problem 16

An alternating voltage $V=140 \sin 50 t$ is applied to a resistor of resistance $10 \Omega$. This voltage produces $\Delta H$ heat in the resistor in time $\Delta t$. To produce the same heat in the same time, required D.C. current is :
(a) $14 \mathrm{~A}$
(b) about $20 \mathrm{~A}$
(c) about $10 \mathrm{~A}$.
(d) none of these

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02:45

Problem 17

An A.C. is represented by $e=220 \sin (100 \pi) t$ volt and is applied over a resistance of $110 \mathrm{ohm} .$ The heat produced in 7 minutes is :
(a) $11 \times 10^{3}$ cal
(b) $22 \times 10^{3}$ cal
(c) $33 \times 10^{3} \mathrm{cal}$
(d) $25 \times 10^{3}$ cal

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01:21

Problem 18

The reactance of a capacitor connected with D.C. voltage is :
(a) zero
(b) infinity
(c) $1 \Omega$
(d) none of these

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01:25

Problem 19

The reactance of an inductor connected with a D.C. voltage is:
(a) zero
(b) $\infty$
(c) $1 \Omega$
(d) none of these

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04:17

Problem 20

An A.C. voltage $e=e_{0} \sin 50 t-e_{0} \cos 100 \pi t$ is connected in series with a resistor and capacitor. The steady state current through circuit is found to be
$I=I_{0} \sin \left(50 \pi t+\phi_{1}\right)+I_{0}^{\prime} \cos \left(100 \pi t+\phi_{2}\right)$
Then the ratio of $\frac{l_{0}}{I_{0}}$ is :
(a) greater than 1
(b) equal to 1
(c) less than 1
(d) none of these

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04:23

Problem 21

In a region of uniform magnetic field $B=10^{-2} \mathrm{~T}$, a circular coil is rotating at '\omega' rpm about an axis which is perpendicular to the direction of ' $B^{\prime}$ and which forms a diameter of the coil. The radius of the coil is $30 \mathrm{~cm}$ and resistance $\pi^{2}$ ohm. If the amplitude of the alternating current induced in the coil is $6 \mathrm{~mA}$, then value of ' $\omega^{\prime}$ is :
(a) $15 \mathrm{rpm}$
(b) $300 \mathrm{rpm}$
(c) $21 \mathrm{rpm}$
(d) $400 \mathrm{rpm}$

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01:59

Problem 22

An alternating voltage $V=V_{0} \sin \omega t$ is connected to a capacitor of capacity $C_{0}$ through an A.C. ammeter of zero resistance. The reading of ammeter is:
(a) $\frac{V_{0}}{\sqrt{2}}$
(b) $\frac{V_{0}}{\omega C \sqrt{2}}$
(c) $\frac{V_{0} \omega C}{\sqrt{2}}$
(d) none of these

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02:17

Problem 23

Which one of the following represents capacitive reactance versus angular frequency graph?

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02:46

Problem 24

Which of the following plots may represent the reactance of a series $L-C$ combination?

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03:47

Problem 25

The maximum current in the circuit, if a capacitor of capacitance $1 \mu \mathrm{F}$ is charged to a potential of $2 \mathrm{~V}$ and is connected in parallel to an inductor of inductance $10^{-3} \mathrm{H}$, is :
(a) $\sqrt{4000} \mathrm{~mA}$
(b) $\sqrt{2000} \mathrm{~mA}$
(c) $\sqrt{1000} \mathrm{~mA}$
(d) $\sqrt{5000} \mathrm{~mA}$

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05:27

Problem 26

In a circuit consisting of inductor $(L)$, capacitor (C) and resistor $(R)$ are in series, if $\omega L<\frac{1}{\omega C}$, then the emf:
(a) leads the current
(b) lags behind the current
(c) is in phase with current
(d) is zero

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04:49

Problem 27

In a circuit, a resistance of $20000 \mathrm{ohm}$ is connected to a capacitor of capacity of $0.1 \mu \mathrm{F}$ in parallel. A voltage of 20 volt and $f=50 \mathrm{~Hz}$ is connected across the arrangement. The main current is :
(a) $117 \mathrm{~mA}$
(b) $1.18 \mathrm{~mA}$
(c) $11.7 \mathrm{~mA}$
(d) $0.117 \mathrm{~mA}$

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03:39

Problem 28

The resonant frequency of a series circuit consisting of an inductance $200 \mu \mathrm{H}$, a capacitance of $0.0005 \mu \mathrm{F}$ and a resistance of $10 \Omega$ is :
(a) $480 \mathrm{kHz}$
(b) $503 \mathrm{kHz}$
(c) $406 \mathrm{kHz}$
(d) $607 \mathrm{kHz}$

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01:46

Problem 29

The frequency of voltage for an A.C. circuit, the equation of alternating voltage is $V=200 \sin 314 t$ is :
(a) $50 \mathrm{~Hz}$
(b) $60 \mathrm{~Hz}$
(c) $55 \mathrm{~Hz}$
(d) $65 \mathrm{~Hz}$

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03:19

Problem 30

An A.C. circuit with $f=1000 \mathrm{~Hz}$ consists of a coil of 200 millihenry and negligible resistance. The voltage across the coil, if the effective current of $5 \mathrm{~mA}$ is flowing, is :
(a) $7.64 \mathrm{~V}_{(\mathrm{rms})}$
(b) $7.452 \cdot \mathrm{v}_{(\mathrm{rms})}$
(c) $6.28 \mathrm{~V}_{(\mathrm{rms})}$
(d) $74.62 \mathrm{v}_{(\mathrm{rms})}$

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04:14

Problem 31

An A.C. circuit consists of a resistance and a choke in series. The resistance is of $220 \Omega$ and choke is of $0.7$ henry. The power absorbed from 220 volts and $50 \mathrm{~Hz}$, source connected with the circuit, is:
(a) $120.08$ watt
(b) $109.97$ watt
(c) $100.08$ watt
(d) $98.08$ watt

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02:13

Problem 32

If a circuit made up of a resistance $1 \Omega$ and inductance $0.01 \mathrm{H}$, an alternating emf 200 volt at $50 \mathrm{~Hz}$ is connected, then the phase difference between the current and the $\mathrm{emf}$ in the circuit is :
(a) $\tan ^{-1}(\pi)$
(b) $\tan ^{-1}\left(\frac{\pi}{2}\right)$
(c) $\tan ^{-1}\left(\frac{\pi}{1}\right)$
(d) $\tan ^{-1}\left(\frac{\pi}{3}\right)$

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01:58

Problem 33

In the series LCR circuit, the voltmeter and ammeter readings are respectively :
(a) $V=250 \mathrm{~V}, I=4 \mathrm{~A}$
(b) $V=150 \mathrm{~V}, I=2 \mathrm{~A}$
(c) $V=1000 \mathrm{~V}, I=5 \mathrm{~A}$
(d) $V=100 \mathrm{~V}, I=2 \mathrm{~A}$

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01:52

Problem 34

The current in resistance $R$ at resonance is
(a) zero
(b) minimum but finite
(c) maximum but finite
(d) infinite

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02:52

Problem 35

An inductor $L$, a capacitor $C$ and ammeters $A_{1}, A_{2}$ and $A_{3}$ are connected to an oscillator in the circuit as shown in the adjoining figure
When frequency of the oscillator is increased, then at resonant frequency, the ammeter reading is zero in the case of:
(a) ammeter $A_{1}$
(b) ammeter $A_{2}$
(c) ammeter $A_{3}$
(d) all the three

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01:38

Problem 36

A r?sistor $R$, an inductor $L$, a capacitor $C$ and voltmeters $V_{1}, V_{2}$ and $V_{3}$ are
connected to an oscillator in the circuit as shown in the following diagram. When the frequency of the oscillator is increased, then at resonance frequency, the voltmeter reading is zero in the case of :
(a) voltmeter $V_{1}$
(b) voltmeter $V_{2}$
(c) voltmeter $V_{3}$
(d) all the three voltmeters

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01:50

Problem 37

At resonance, in the circuit:
(a) the power factor is zero
(b) the current through the A.C. source is zero
(c) the current through the A.C. source is maximum
(d) currents through $L$ and $R$ are equal

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03:18

Problem 38

A condenser of capacitance of $2.4 \mu \mathrm{F}$ is used in a transmitter to transmit at $\lambda$ wavelength. If the inductor of $10^{-8} \mathrm{H}$ is used for resonant circuit, then value of $\lambda$ is :
(a) $292 \mathrm{~m}$
(b) $400 \mathrm{~m}$
(c) $334 \mathrm{~m}$
(d) $446 \mathrm{~m}$

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02:04

Problem 39

If $20 \mathrm{~V}$ battery is connected to primary coil of a transformer, then output voltage is:
(a) zero
(b) $20 \mathrm{~V}$
(c) $10 \mathrm{~V}$
(d) none of these

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03:19

Problem 40

If a dry cell of $\mathrm{emf}=1.5 \mathrm{~V}$ is connected across the primary of a step-up transformer of turn ratio $3: 5$, then the voltage developed across the secondary is :
(a) $30 \mathrm{~V}$
(b) $5 \mathrm{~V}$
(c) zero
(d) $2.5 \mathrm{~V}$

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02:16

Problem 41

An A.C. source has an internal resistance of $10^{4}$ ohm. The turn ratio of a transformer so as to match the source to a load of resistance $10 \mathrm{ohm}$, is :
(a) $4.62 \times 10^{-2}$
(b) $2.03 \times 10^{-2}$
(c) $3.16 \times 10^{-2}$
(d) $5.62 \times 10^{-2}$

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01:54

Problem 42

An output voltage of $E=170 \sin 377 t$ is produced by an
A.C. generator, where $t$ is in sec, then the frequency of alternating voltage will be:
(a) $50 \mathrm{~Hz}$
(b) $110 \mathrm{~Hz}$
(c) $60 \mathrm{~Hz}$
(d) $230 \mathrm{~Hz}$

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02:18

Problem 43

The electric field ' $E^{\prime}$ and magnetic field ' $B^{\prime}$ in electromagnetic waves are:
(a) parallel to each other
(b) inclined at an angle of $45^{\circ}$
(c) perpendicular to each other
(d) opposite to each other

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01:55

Problem 44

The energy of photon of electromagnetic radiation of wavelength $=2000 \AA$ is :
(a) $1.76 \times 10^{-18} \mathrm{~J}$
(b) $0.99 \times 10^{-18} \mathrm{~J}$
(c) $0.54 \times 10^{-18} \mathrm{~J}$
(d) $0.63 \times 10^{-18} \mathrm{~J}$

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03:07

Problem 45

The speed of light in air, if an electromagnetic wave is travelling in air whose dielectric constant is $k=1.006$, will be:
(a) $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(b) $3.88 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(c) $2.5 \times 10^{8} \mathrm{~m} / \mathrm{s}$
(d) $4.6 \times 10^{8} \mathrm{~m} / \mathrm{s}$

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03:04

Problem 46

An object is placed at some distance from a radio station. If the interval between transmission and reception of pulses is $2.66 \times 10^{-2} \mathrm{sec}$, then the distance is :
(a) $4000 \mathrm{~km}$
(b) $2000 \mathrm{~km}$
(c) $3000 \mathrm{~km}$
(d) $2500 \mathrm{~km}$

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01:31

Problem 47

The wavelength of a radio wave of frequency of $1 \mathrm{MHz}$ is :
(a) $400 \mathrm{~m}$
(b) $300 \mathrm{~m}$
(c) $350 \mathrm{~m}$
(d) $200 \mathrm{~m}$

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01:43

Problem 48

Some radio waves of frequency of about $1.5 \times 10^{9} \mathrm{~Hz}$ was received by a radio-telescope from distant star. If the speed of the waves is $3 \times 10^{5} \mathrm{~km} / \mathrm{s}$, then the wave- length of the wave will be:
(a) $0.1 \mathrm{~m}$
(b) $0.6 \mathrm{~m}$
(c) $0.2 \mathrm{~m}$
(d) $0.46 \mathrm{~m}$

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02:31

Problem 49

A radio wave of intensity 1 is reflected by a surface. The intensity $(I)$, if pressure exerted on the surface is $2 \times 10^{-8} \mathrm{~N} / \mathrm{m}^{2}$, will be :
(a) $3 \mathrm{~N} / \mathrm{m}^{2}$
(b) $4 \mathrm{~N} / \mathrm{m}^{2}$
(c) $6 \mathrm{~N} / \mathrm{m}^{2}$
(d) $7 \mathrm{~N} / \mathrm{m}^{2}$

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04:06

Problem 50

A TV tower has a height of $100 \mathrm{~m}$. The area covered by the TV broadcast, if radius of the earth is $6400 \mathrm{~km}$, will be :
(a) $380 \times 10^{7} \mathrm{~m}^{2}$
(b) $402 \times 10^{7} \mathrm{~m}^{2}$
(c) $595 \times 10^{7} \mathrm{~m}^{2}$
(d) $440 \times 10^{7} \mathrm{~m}^{2}$

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03:13

Problem 51

An electromagnetic wave with pointing vector $5 \mathrm{~W} / \mathrm{m}^{2}$ is absorbed by a surface of some area. If the force on the surface is $10^{-7} \mathrm{~N}$, then area is:
(a) $6 \mathrm{~m}^{2}$
(b) $3 \mathrm{~m}^{2}$
(c) $60 \mathrm{~m}^{2}$
(d) $4 \mathrm{~m}^{2}$

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02:13

Problem 52

The average power per unit area at distance of $2 \mathrm{~m}$ from a small bulb, if the bulb emits $20 \mathrm{~W}$ of electromagnetic radiation uniformly in all directions, will be :
(a) $0.69 \mathrm{~W} / \mathrm{m}^{2}$
(b) $0.56 \mathrm{~W} / \mathrm{m}^{2}$
(c) $0.78 \mathrm{~W} / \mathrm{m}^{2}$
(d) $0.39 \mathrm{~W} / \mathrm{m}^{2}$

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02:22

Problem 53

The correct option, if speed of gamma rays, $X$ -rays and microwaves are $v_{g^{\prime}} v_{x}$ and $v_{m}$ respectively will be :
(a) $v_{g}>v_{x}>v_{m}$
(b) $v_{g}<v_{x}<v_{m}$
(c) $v_{g}>v_{x}<v_{m}$
(d) $v_{g}=v_{x}=v_{m}$

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02:22

Problem 53

The correct option, if speed of gamma rays, $X$ -rays and microwaves are $v_{g^{\prime}} v_{x}$ and $v_{m}$ respectively will be :
(a) $v_{g}>v_{x}>v_{m}$
(b) $v_{g}<v_{x}<v_{m}$
(c) $v_{g}>v_{x}<v_{m}$
(d) $v_{g}=v_{x}=v_{m}$

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01:35

Problem 54

If at a certain instant, the magnetic induction of the electromagnetic wave in vacuum is $6.7 \times 10^{-12} \mathrm{~T}$, then the magnitude of electric field intensity will be:
(a) $2 \times 10^{-3} \mathrm{~N} / \mathrm{C}$
(b) $3 \times 10^{-3} \mathrm{~N} / \mathrm{C}$
(c) $4 \times 10^{-3} \mathrm{~N} / \mathrm{C}$
(d) $1 \times 10^{-3} \mathrm{~N} / \mathrm{C}$

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