Alternating Current Test

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Alternating Current Test - 68

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Weekly Quiz Competition

Question 1
1 / -0

In an ac circuit the reactance of a coil is $$ \sqrt{3} $$ times its resistance, the phase difference between the voltage across the coil to the current through the coil will be

A
$$ \dfrac{\pi}{3} $$

B
$$ \dfrac{\pi}{2} $$

C
$$ \dfrac{\pi}{4} $$

D
$$ \dfrac{\pi}{6} $$

Solution

As we know,
$$ tan \phi = \dfrac{X_L}{R} = \dfrac{\sqrt{3}R}{R} = \sqrt{3} $$ $$ \Rightarrow \, \phi = 60^{\circ} = \dfrac{\pi}{3} $$
Question 2
1 / -0

In series $$LCR$$ circuit, in the condition of resonance, if $$C=1\mu F;L=1H$$ then frequency will be:

A
$${ 10 }^{ 6 }Hz$$

B
$$2\pi \times { 10 }^{ 6 }Hz$$

C
$$\cfrac { { 10 }^{ 6 } }{ 2\pi } Hz$$

D
$$2\pi \times { 10 }^{ -6 }Hz$$

Solution

$$\omega =\cfrac { 1 }{ \sqrt { LC } } \Rightarrow f=\cfrac { 1 }{ 2\pi \sqrt { LC } } =\cfrac { 1 }{ 2\pi \times \sqrt { { 10 }^{ -6 }\times { 10 }^{ -6 } } } =\cfrac { { 10 }^{ 6 } }{ 2\pi } Hz$$
Question 3
1 / -0

Which of the following components of a LCR circuit with ac supply dissipates energy

A
L

B
R

C
C

D
All of these

Solution

Resistor is the components of a LCR circuit, with ac supply ,dissipates energy as $$E=i^2Rt$$
And inductor and capacitor stores energy in form of magnetic and electric field energy.
Question 4
1 / -0

A resistance of $$ 40 $$ ohm and an inductance of $$ 95.5 $$ millihenry are connected in series in a $$ 50 $$ cycles/second ac circuit. The impedance of this combination is very nearly

A
$$ 30 \,ohm $$

B
$$ 40 \, ohm $$

C
$$ 50 \, ohm $$

D
$$ 60 \, ohm $$

Solution

As we know,

$$ Z = \sqrt{R^2 + (2 \pi \nu L)^2} $$

$$ = \sqrt{(40)^2 + 4 \pi^2 \times (50)^2 \times (95.5 \times 10^{-3})^2} = 50\, ohm $$
Question 5
1 / -0

A coil of $$ 200 \, \Omega $$ resistance and $$ 1.0 H $$ inductance is connected to an ac source of frequency $$ \dfrac{200}{2 \pi} \, Hz $$. Phase angle between potential and current will be

A
$$ 30^{\circ} $$

B
$$ 90^{\circ} $$

C
$$ 45^{\circ} $$

D
$$ 0^{\circ} $$

Solution

As we know,

$$ tan \phi = \dfrac{X_L}{R} = \dfrac{2 \pi \nu L}{R} = \dfrac{2 \pi \times \dfrac{200}{2 \pi} \times 1}{200} = 1 $$ $$ \Rightarrow \, \phi = 45^{\circ} $$
Question 6
1 / -0

An alternating current circuit is in resonance at $$10kHz$$ frequency. If frequency increases to $$12kHz$$, then what will be effect on impedance?

A
remains unchanged

B
increases $$1.2$$ times

C
increases and becomes capacitive

D
increases and becomes inductive

Solution

In the condition of resonance $$Z=R$$, so impedance is not dependent on the frequency.
Question 7
1 / -0

The current lags behind the voltage by a phase different of $$\pi /2$$ radian, when in the circuit is:

A
only resistance

B
only inductance

C
only capacitor

D
both capacitor and resistance
Solution
- In inductor current lag behind the voltage by a phase difference
Question 8
1 / -0

Which of the following is used in a circuit which shows that the current lead the voltage at the phase:

A
pure resistance

B
pure inductance

C
pure capacitor

D
none of these

Solution

Pure capacitor
Question 9
1 / -0

The reactance of a capacitor of capacitance C is X. If both the frequency and capacitance be doubled, then new reactance will be

A
$$X$$

B
$$2X$$

C
$$4X$$

D
$$\frac{X}{4}$$

Solution

$$X_{c}=X$$
When both capacitance frequency are doubled the reactance will become
$$X_{C}^{'}=\frac{1}{2\pi \times (2f) \times (2C)}=\frac{1}{4} \times \frac{1}{2\pi fC}=\frac{X}{4}$$
Question 10
1 / -0

A sinusoidally varying potential difference has amplitude $$170 \,V$$. What is its rms value?

A
$$170 \,V$$

B
$$170 \,V$$

C
$$0$$

D
$$-120 \,V$$

E
$$-170 \,V$$

Solution

$$\Delta V_{rms}=\Delta V_{max}/\sqrt{2}=170/\sqrt{2}=120 \,V$$

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Re-Attempt Weekly Quiz Competition

Alternating Current Test - 68

Result

Alternating Current Test - 68

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Question 1

$$ \dfrac{\pi}{3} $$

$$ \dfrac{\pi}{2} $$

$$ \dfrac{\pi}{4} $$

$$ \dfrac{\pi}{6} $$

Solution

Question 2

$${ 10 }^{ 6 }Hz$$

$$2\pi \times { 10 }^{ 6 }Hz$$

$$\cfrac { { 10 }^{ 6 } }{ 2\pi } Hz$$

$$2\pi \times { 10 }^{ -6 }Hz$$

Solution

Question 3

L

R

C

All of these

Solution

Question 4

$$ 30 \,ohm $$

$$ 40 \, ohm $$

$$ 50 \, ohm $$

$$ 60 \, ohm $$

Solution

Question 5

$$ 30^{\circ} $$

$$ 90^{\circ} $$

$$ 45^{\circ} $$

$$ 0^{\circ} $$

Solution

Question 6

remains unchanged

increases $$1.2$$ times

increases and becomes capacitive

increases and becomes inductive

Solution

Question 7

only resistance

only inductance

only capacitor

both capacitor and resistance

Solution

Question 8

pure resistance

pure inductance

pure capacitor

none of these

Solution

Question 9

$$X$$

$$2X$$

$$4X$$

$$\frac{X}{4}$$

Solution

Question 10

$$170 \,V$$

$$170 \,V$$

$$0$$

$$-120 \,V$$

$$-170 \,V$$

Solution

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