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Sinusoidal current - class-X

Description: sinusoidal current
Number of Questions: 18
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Tags: physics electric charge and electric current electricity and magnetism electromagnetic induction and alternating currents alternating currents magnetic effects of electric current
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A 220 V, 50 Hz AC source is connected to an inductance of 0.2 H and resistance of 20 $\Omega$ in series. The current in the circuit is :

physics alternating currents sinusoidal current types of current movement of charge

  1. $3.33 A$

  2. $33.3 A$

  3. $15 A$

  4. $5 A$

Show answer
Correct Option: A
Explanation:

Given, V =220 volts, f=50 Hz, L =0.2 H, R = 20 $\Omega$


$X _L =2\pi fL=2 \times 3.14 \times 50 \times 0.2$

$= 100 \times  0.628 = 62.80\Omega$

$Z = \sqrt{X^2 _L + R^2} = \sqrt{(62.8)^2 + 20^2}$

$I = \displaystyle \frac{V}{Z} = \frac{220}{\sqrt{43473.84}} = 3.33A$

An alternating voltage $E=200\sqrt{2}\sin (100t)$ is connected to $1$ microfarad capacitor through AC ammeter. The reading of ammeter shall be.

physics alternating currents sinusoidal current types of current movement of charge

  1. $10$mA

  2. $20$mA

  3. $40$mA

  4. $80$mA

Show answer
Correct Option: B
Explanation:

Reading of ammeter $=I _{rms}=\displaystyle \frac{V _{rms}}{X _C}=\frac{V _0\omega C}{\sqrt 2}$
$=\displaystyle\frac{200\sqrt 2\times 100\times (1\times 10^{-6})}{\sqrt 2}=2\times 10^{-2} A$
$=20 mA$

The frequency of A.C mains in India is

physics alternating currents sinusoidal current types of current movement of charge

  1. $30 Hz$

  2. $50Hz$

  3. $60Hz$

  4. $120Hz$

Show answer
Correct Option: B
Explanation:
Frequency of AC mains in India is $50 Hz$,similar to most European countries. Whereas USA uses $60 Hz$

A bulb  is connected  to an ideal battery of emf 10 V so that the resulting current is 10 mA . When the bulb is connected to 220 V mains (ideal), the current is 50 mA. choose the correct alternative

physics alternating currents sinusoidal current types of current movement of charge

  1.   the resistance of the bulb is 1 k ohm and in the second case, it is 4.4 k ohm

  2. it is not possible since ohm's law is not followed

  3.  the increase in resistance is due to heating of the filament of the bulb when it is connected to 220 V main

  4. none of these

Show answer
Correct Option: A
Explanation:

A bulb is connected to an ideal battery of emf$=10V$

Current$=10mA\=10\times10^{-3}A$
when the bulb connected $220V$ (main)
and current$=50\times10^{-3}A$
Using Ohm's law,
First case:
$I=\cfrac{10\times10^3}{10}=1K\Omega$
Second case 
$I^{\prime}=\cfrac{220\times10^3}{50}=4.4k\Omega$
Hence answer $(A)$ will be correct.

In a transformer the immediate cause of the induced A. C. in the secondary coil is

physics alternating currents sinusoidal current types of current movement of charge

  1. A varying electric field

  2. A varying magnetic field

  3. A motion of the secondary coil

  4. Efficiency of the operator

Show answer
Correct Option: B

Alternating current is one which changes in its :

physics alternating currents sinusoidal current types of current movement of charge

  1. direction

  2. magnitude

  3. magnitude and direction both

  4. none

Show answer
Correct Option: C
Explanation:

Answer is C.

An alternating current (AC) is an electric current of which magnitude and direction vary, unlike direct current, whose direction remains constant.
The usual waveform of an AC power circuit is a sine wave, because this leads to the most efficient transmission of energy. However, in certain applications different waveforms are used, such as triangular or square waves.

An alternating voltage is given by $e = (6\sin \omega t + 8\cos \omega t)volt$. The instantaneous value of voltage is given by

physics alternating currents sinusoidal current types of current movement of charge

  1. $5\sqrt {2}V$

  2. $10V$

  3. $10\sqrt {2}V$

  4. $\dfrac {10}{\sqrt {2}}V$

Show answer
Correct Option: B

State whether given statement is True or False
The designation rms means repetitions measured per second.

physics alternating currents sinusoidal current types of current movement of charge

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

The dsignation rms means Root Mean Square Value of a quantity such as RMS value of current, voltage in an ac circuit.

The simplest type of AC voltage or current is the one which

physics alternating currents sinusoidal current types of current movement of charge

  1. Varies exponentially

  2. Varies sinusoidally

  3. Varies linearly

  4. Does not vary uniformly

Show answer
Correct Option: B
Explanation:

Solution:-

AC wave can be of any form but mathematical techniques are easier for the sine waveform such as any wave can be represent as combination of sine waves using fourier transform and integration and differentiation of sine wave is sine wave only.

Option B is correct.

Choose the incorrect statement.

physics alternating currents sinusoidal current types of current movement of charge

  1. Alternating current is oscillatory

  2. Electric power is transmitted over long distances using alternating current.

  3. Frequency of alternating current in India is 50 Hz.

  4. Alternating current can be used for electrolysis of copper chloride.

Show answer
Correct Option: D
Explanation:

Even if it were current-limited, alternating current (AC) would not be appropriate for electrolysis. Because the "cathode" and "anode" will be constantly switching places as the polarities will change with time. Therefore, direct current (DC) is used for electrolysis.

Why the current produced by the generator is  called as alternating current.

physics alternating currents sinusoidal current types of current movement of charge

  1. continuous decrease and increase of current occurs.

  2. after every half cycle direction of flow of current is reversed.

  3. both

  4. none

Show answer
Correct Option: B
Explanation:

We may say that after every half cycle direction of flow of current is reversed. Because of this reason the current produced by the generator is also called as alternating current.

A coil, a capacitor and an ac source of rms voltage $24V$ are connected in series. By varying the frequency of the source, a maximum rms current of $6A$ is observed. If this coil is connected to a battery of emf $12V$ and internal resistance $4\Omega$, the current through will be

physics alternating currents sinusoidal current types of current movement of charge

  1. $2.4A$

  2. $1.8A$

  3. $1.5A$

  4. $1.2A$

Show answer
Correct Option: C

A mixer of $1000\Omega$ resistance is connected to an $A.C.$ source of $200\ volts$ and $50\ cycle/sec$. The value of average potential difference across the mixer will be:

physics alternating currents sinusoidal current types of current movement of charge

  1. $308\ volts$

  2. $264\ volts$

  3. $220\ volts$

  4. $zero$

Show answer
Correct Option: D

Choose the correct statements from the following $A.C.$ cannot be used in

physics alternating currents sinusoidal current types of current movement of charge

  1. Electroplating

  2. Charging a battery

  3. Charging a capacitor

  4. Electrolysis

  5. Heating a room

Show answer
Correct Option: A

Two alternating currents having value $I _{1} = 3\sin \omega t$ and $I _{2} = 4\sin \left (\dfrac {\pi}{2} - \omega \right )$ are superimposed and passed through a hot wire ammeter. Then the roading of ammeter will be

physics alternating currents sinusoidal current types of current movement of charge

  1. $5A$

  2. $-\dfrac {5}{\sqrt {2}}A$

  3. $7A$

  4. $\dfrac {7}{\sqrt {2}}A$

Show answer
Correct Option: C

In alternating current

physics alternating currents sinusoidal current types of current movement of charge

  1. The direction of current is always positive

  2. The direction of current is always negative

  3. The direction of current changes constantly

  4. The direction of current is either positive or negative

Show answer
Correct Option: C
Explanation:

C

Electric charge in alternating current (AC) changes direction periodically. The voltage in AC circuits also periodically reverses because the current changes direction.

 

An alternating current is that current which changes regularly its

physics alternating currents sinusoidal current types of current movement of charge

  1. Magnitude

  2. Direction

  3. Both a and b

  4. None of the above

Show answer
Correct Option: C

In an A.C. circuit a resistance R is connected in series with an inductance L.The phase difference between voltage and current is $45^o$. Then what will be the value of inductive reactance?

physics alternating currents sinusoidal current types of current movement of charge

  1. R

  2. $\frac{R}{2}$

  3. $\frac{R}{4}$

  4. 2R

Show answer
Correct Option: A
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