Alternating Current Test

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Alternating Current Test - 22

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Weekly Quiz Competition

Question 1
1 / -0

The correct curve between inductive reactance (XL) and frequency (f) is

A

B

C

D

Solution

Since,
$${ X }_{ L }=2\pi fL$$
therefore its a linear graph hence option(B) is correct
Question 2
1 / -0

When the values of inductance and capacitance in an $$L-C$$ circuit are $$0.5\ H$$ and $$8\ \mu$$F respectively then current in the circuit is maximum. The angular frequency of alternating e.m.f. applied in the circuit will be

A
$$\displaystyle 5 \times 10^3\ Radian/sec$$

B
$$50\ Radian/sec$$

C
$$\displaystyle 5 \times 10^2\ Radian/sec$$

D
$$5\ Radian/sec$$

Solution

We know that, maximum current flows when the circuit is at resonance
Therefore, Resonance frequency is given by

$$\omega =\dfrac { 1 }{ \sqrt { LC } } $$

$$\omega =\dfrac { 1 }{ \sqrt { 0.5\times 8\times { 10 }^{ -6 } } } $$

this gives

$$\omega =5\times { 10 }^{ 2 }$$ Radian/sec
Question 3
1 / -0

The inductive reactance of a coil is $$2500\ \Omega$$. On increasing its self-inductance three times, the new inductive reactance will be

A
$$7500\ \Omega$$

B
$$2500\ \Omega$$

C
$$1225\ \Omega$$

D
$$zero$$

Solution

We know that ,
$${ X }_{ L }=\omega L$$
therefore when $$L$$ is made three times inductive reactance will also become three times.
Therefore new reactance will be equal to $$3\times 2500\ \Omega=7500\ \Omega$$.
Question 4
1 / -0

The inductive reactance of a choke coil of $$\displaystyle 1/4 \pi\ mH$$ in an $$AC$$ circuit of $$50\ Hz,$$ will be

A
25 ohm

B
0.25 ohm

C
0.025 ohm

D
2.5 ohm

Solution

$${ X }_{ L }=\omega L$$

$${ X }_{ L }==2\pi fL$$

$${ X }_{ L }=2\pi \times 50\times \dfrac { { 10 }^{ -3 } }{ 4\pi } $$

$${ X }_{ L }=0.025\ \Omega $$
Question 5
1 / -0

The value of alternating emf in the following circuit will be

A
220 volt

B
140 volt

C
20 volt

D
100 volt

Solution

$$V=\sqrt { { V }_{ R }^{ 2 }+{ ({ V }_{ L }^{ }-{ V }_{ C }^{ }) }^{ 2 } } $$

$$V=\sqrt { { 80}^{ 2 }+{ (40^{ }-100^{ }) }^{ 2 } } $$

$$V=100$$ volt
Question 6
1 / -0

The correct curve between the resistance of a conductor (R) and frequency (f) is

A

B

C

D

Solution

The resistance of a resistor is independent of the frequency of the AC source to which it is connected. Thus it has a constant curve against frequency.
However the impedance of an inductor or a capacitor changes with the frequency of the AC source.

Impedance of an inductor $$=\omega L=2\pi fL$$

Impedance of a capacitor $$=\dfrac{1}{\omega C}=\dfrac{1}{2\pi fC}$$
Question 7
1 / -0

The capacitive reactance at $$1600\ Hz$$ is $$81\ \Omega$$. When the frequency is doubled then capacitive reactance will be

A
$$40.5\ \Omega$$

B
$$81\ \Omega$$

C
$$162\ \Omega$$

D
$$Zero$$

Solution

capacitive reactance is inversely proportional to the frequency
$${ X }_{ C }=\dfrac{1}{2\pi fC}$$
therefore when frequency is doubled capacitive reactance will get halved therefore new $${ X }_{ C }$$ is $$40.5\ \Omega $$
Question 8
1 / -0

An $$R-C$$ circuit is as shown in the following diagram.The capacity reactance and impedance will be

A
zero

B
infinity

C
$$\displaystyle \frac{1}{\omega c}$$

D
$$\displaystyle \omega c$$

Solution

Since power source is dc therefore,

$$\omega =0 $$

$${ X }_{ C }=\dfrac { 1 }{ \omega C } $$

$${ X }_{ C }=\dfrac { 1 }{0}$$

$${ X }_{ C }=\infty $$

$$Z=\infty$$
Question 9
1 / -0

An alternating voltage frequency $$\omega$$ is induced in electric circuit consisting of an inductance $$L$$ and capacitance $$C$$, connected in parallel. Then across the inductance coil the
(i) current is maximum when $${\omega}^{2}=1/(LC)$$
(ii) current is minimum when $${\omega}^{2}=1/(LC)$$
(iii) voltage is minimum when $${\omega}^{2}=1/(LC)$$
(iv) voltage is maximum when $${\omega}^{2}=1/(LC)$$

A
(i) and (iii) are correct

B
(i) and (iv) are correct

C
(ii) and (iii) are correct

D
(ii) and (iv) are correct

Solution

In parallel LC circuits, current is minimum when, $$\omega =\sqrt{\dfrac{1}{LC}}$$

Also, current and voltage are at angle of 90 degrees.
Hence, voltage is maximum when current is minimum.
Option D is thus correct.
Question 10
1 / -0

Of the following about capacitive reactance which is correct?

A
The reactance of the capacitor is directly proportional to its ability to store charge

B
Capacitive reactance is inversely proportional to the frequency of the current

C
Capacitive reactance is measured in farad

D
The reactance of a capacitor in an AC circuit is similar to the resistance of a capacitor in a DC circuit

Solution

Capacitative reactance is an opposition to the change of voltage across an element.
It is denoted by $$X_C$$ and is inversely proportional to the signal frequency(f) and the capacitance C.
$$X_C=\dfrac{1}{2\pi fC}$$