Alternating Current Test

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Alternating Current Test - 82

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Question 1
1 / -0

From the figure shown, a series L-C-R circuit connected to a variable frequency $$200\, V$$ source. $$L=5H,\, C=80\, \mu F$$ and $$R=40 \Omega$$. Then the source frequency which drives the circuit at resonance is

A
$$25\, Hz$$

B
$$\frac {25}{\pi}\, Hz$$

C
$$50\, Hz$$

D
$$\frac {50}{\pi}\, Hz$$

Solution
Question 2
1 / -0

In a series LCR circuit K = 200 S2 and the voltage and frequency of the main supply are 220 V and 50 Hz respectively. On taking out the capacitor from the circuit, the current leads the voltage by 30. On taking out the indicator from the circuit the current leads the voltage by 30. The power dissipated in the LCR circuit is :

A
342 W

B
305 K

C
209 K

D
242 K

Solution
Question 3
1 / -0

In an AC circuit instantaneous current is given by $$i=i_0sin\dfrac{\pi}{6}t.$$ The time from starting when current in circuit becomes equal to its rms value for the first time is

A
$$1.5s$$

B
$$2s$$

C
$$2.5s$$

D
$$3s$$

Solution
Question 4
1 / -0

The power factor of a circuit in which a box having unknown electrical devices connected in series with a resistor of resistance $$3\Omega$$ is $$3/5$$. The reactance of the box is

A
$$5\Omega$$

B

$$\dfrac{5}{3\omega }$$

C
$$4\Omega$$

D

$$\dfrac{4}{3\omega }$$

Solution
Question 5
1 / -0

A potential difference of $$6V$$ is applied to a coil of inductance $$0.5\ H$$ and a resistance of $$4\ ohm$$ connected in series. The time taken for the current to reach half is maximum value is (in seconds).

A
$$\dfrac {\log_{e}{2}}{8}$$

B
$$\dfrac {\log_{e}{2}}{4}$$

C
$$\dfrac {\log_{e}{4}}{8}$$

D
$$\dfrac {\log_{e}{8}}{4}$$

Solution
Question 6
1 / -0

In a series resonant LCR circuit, the voltage across $$ R $$ is 100$$ V $$ and $$ R= $$ 1$$ k \Omega $$ with $$ C $$ $$ =2 \mu F . \operatorname{The} $$ resonant frequency $$ \omega $$ is 200 $$ \mathrm{rad} / \mathrm{s} $$ . At resonance the voltage across L is:

A
$$ 25 \times 10^{-2} V $$

B
$$40$$ $$ V $$

C
$$250$$ $$ \mathrm{V} $$

D
$$ 4 \times 10^{-3} \mathrm{V} $$

Solution
Question 7
1 / -0

Growth of current in two different L-R circuit are depicted by the I-t graphs shown. Angle subtended by the curves with time axis at time t=0 are also shown in the graph $${ \tau }_{ 1 }$$ and $${ \tau }_{ 2 }$$ are time constants for the circuits 1 and 2 respectively. Choose the CORRECT alternative

A
$$\frac { { \tau }_{ 1 } }{ { \tau }_{ 2 } } =\frac { 2 }{ 3 } $$

B
$$\frac { { \tau }_{ 1 } }{ { \tau }_{ 2 } } =\frac { 3 }{ 2 } $$

C
Initial rate of change of current for circuit-2 is 2 times that of circuit-1

D
Initial rate of change of current for circuit-2 is 4 times that of circuit-1
Question 8
1 / -0

Which of the following combinations should be selected for better tunning of an $$LCR$$ circuit used for communication

A
$$ R=20 \Omega, L= $$ $$ =1.5 H, C=35 \mu $$

B
$$ R=25 \Omega $$ $$ L=2.5 H $$,$$ C=45 \mu F $$

C
$$ R=15 \Omega, L=3.5 H, C=30 \mu F $$

D
$$ R=25 \Omega, L $$ $$ =1.5 H, C= $$ $$45$$ $$ \mu F $$

Solution
Question 9
1 / -0

The equation of an alternating voltage is $$V = 220\sin \left [\omega t + \dfrac {\pi}{6}\right ]$$ and the equation for current is $$I = 10\sin \left (\omega t + \dfrac {\pi}{6}\right )$$. The impedance (in ohm) of the circuit is

A
$$11$$

B
$$44$$

C
$$20$$

D
$$22$$

Solution
Question 10
1 / -0

Find the resonant frequency and $$Q-factor$$ of a series $$LCR$$ circuit with $$L = 3.0\ H, C = 27\mu F$$ and $$R = 7.4\Omega$$.

A
$$111\ rad/s, 45$$

B
$$111\ rad/s, 90$$

C
$$55.5\ rad/s, 45$$

D
$$55.5\ rad/s, 90$$

Solution