Alternating Current Test

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Alternating Current Test - 57

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Question 1
1 / -0

For the series LCR circuit shown in the figure, what is the resonance frequency and the amplitude of the current at the resonating frequency.

A
$$2500 rad s^{-1}$$ and $$5\sqrt 2 A$$

B
$$2500 rad s^{-1}$$ and $$5A$$

C
$$2500 rad s^{-1}$$ and $$\frac{5}{\sqrt 2} A$$

D
$$25 rad s^{-1}$$ and $$5\sqrt 2 A$$

Solution

$$\textbf{Hint: At resonance current and voltage are in same phase}$$
$$\textbf{Step1: Find resonating angular frequency}$$
$$\omega = \dfrac{1}{\sqrt{LC}} = \dfrac{1}{\sqrt{8\times 10^{-3}\times 20 \times 10^{-6}}} = 2500 rad/sec$$
$$\textbf{Step2: Find amplitude of current at resonance}$$
Resonance current $$= \dfrac{V}{R} = \dfrac{220}{44} = 5A$$
$$\textbf{Hence option B correct}$$
Question 2
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In the LCR circuit shown in figure unknown resistance and alternating voltage source are connected. When switch $$'S'$$ is closed then there is a phase difference of $$\dfrac {\pi}{4}$$ between current and applied voltage and voltage across resister is $$\dfrac {100}{\sqrt {2}}V$$. When switch is open current and applied voltage are in same phase. Neglecting resistance of connecting wire answer the following questions:
Resonance frequency of circuit is

A
$$50\ Hz$$

B
$$25\ Hz$$

C
$$75\ Hz$$

D
Data insufficient for calculation

Solution
Question 3
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In the L -C circuit shown in figure,the current is in direction shown in the figure and charges on the capacitor plates have sign shown in the figure A this time:-

A
i as well as Q increasing

B
i as well as Q decreasing

C
i is increasing but Q is decreasing

D
i decreasing but Q is increasing

Solution
Question 4
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An alternating current is that current which changes regularly its

A
Magnitude

B
Direction

C
Both a and b

D
None of the above

Solution
Question 5
1 / -0

The voltage across a pure inductor is represented in figure. Which one of the following curves in the figure will represent the current?

A

B

C

D

Solution
Question 6
1 / -0

In a series L-C circuit , if $$L= 10^{-3}$$H and $$C=3 \times 10^{-7}$$ F is connected to a $$100V-50Hz$$ a.c. source, the impedance of the circuit is

A
$$\cfrac{10^5}{3\pi} - 10\pi$$

B
$$0.1\pi - 3\times 10^{-5}\pi$$

C
$$\cfrac{10^5}{3\pi} - \cfrac{\pi}{10}$$

D
None of these

Solution

Impedance $$ Z= \sqrt {R^2 +(X_L - X_C)^2}$$
Where $$ X_L = \omega L$$
$$ X_C = \cfrac{1}{\omega C}$$
and $$ \omega = 2 \pi f$$
$$ =2 \pi \times 50 = 100\pi$$
$$ \therefore X_L = 100 \pi \times 10^{-3} = \cfrac{\pi}{10}$$
$$ X_C = \cfrac{1}{100 \pi \times 3 \times 10^{-7} } = \cfrac{10^5}{3\pi}$$
$$R=0$$
$$\therefore Z=\sqrt{(\cfrac{\pi}{10} - \cfrac{10^5}{3\pi})^2}$$
$$ = \cfrac {10^5}{3\pi} - \cfrac{\pi}{10}$$ As, ($$ \cfrac {10^5}{3\pi} > \cfrac{\pi}{10}$$)
Question 7
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A $$2$$ $$F$$ capacitor is initially charged to $$20$$ $$V$$ and then shorted across a $$5$$ $$mH$$ inductor. The angular frequency of oscillation is.

A
$$1000$$ $${rad/s}$$

B
$$100$$ $${rad/s}$$

C
$$10000$$ $${rad/s}$$

D
$$10$$ $${rad/s}$$

Solution

$$\omega_o=\cfrac{1}{\sqrt{LC}}$$
$$\omega_o=\cfrac{1}{\sqrt{2\times 5\times 10^{-3}}}$$
$$\omega_o=10$$ $${rad/sec}$$
Question 8
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A inductance capacitance circuit is in the state of resonance. if the $$C = 0.1 \mu F$$ and $$L = 0.25$$ Henry. Neglecting ohmic resistance of circuit what is the frequency of oscillations

A
$$1007 \ Hz$$

B
$$100 \ Hz$$

C
$$109 \ Hz$$

D
$$500 \ Hz$$

Solution

From the formula, the frequency of oscillation is

$$f=\dfrac{1}{2\pi\sqrt{LC}}$$

$$=\dfrac{1}{2\pi\sqrt{0.25\times 0.1\times 10^{-6}}}$$

$$=1007\,Hz$$
Question 9
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In a series LCR circuit
$$V_l = 3V_R$$ and $$V_C = 2V_R$$
Volatge across capacitance

A
110 V

B
220 V

C
330 V

D
440 V
Question 10
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In the given circuit the maximum current can be

A
$$\dfrac{E_0}{R}$$

B
$$\dfrac{E_0}{\omega L}$$

C
$$E_0\omega C$$

D
$$\frac{E_0}{\Bigg[ \Big\lgroup \omega L - \dfrac{1}{\omega C} \Big\rgroup^2 + R^2 \Bigg ]^{1/2}}$$

Solution