Alternating Current Test

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Alternating Current Test - 29

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Weekly Quiz Competition

Question 1
1 / -0

If in a series L-C-R ac circuit, the voltages across R, L, C are $$V_{1},V_{2},V_{3}$$ respectively. Then the voltage of applied AC source is always equal to :

A
$$V_{1}+V_{2}+V_{3}$$

B
$$\sqrt{V_{1}^{2}+(V_{2}+V_{3})^{2}}$$

C
$$V_{1}-V_{2}-V_{3}$$

D
$$\sqrt{V_{1}^{2}+(V_{2}-V_{3})^{2}}$$

Solution

$$V_2$$ and $$V_3$$ will be $$180^0$$ out of phase with each other.

Hence, resultant is $$V_2 -V_3$$.

Each of $$V_2$$ and $$V_3$$ is having a phase diff of $$90^0$$ with $$V_1$$.

Hence, resultant AC voltage which is equal to the applied AC voltage is $$\sqrt{ V_1 ^2 + ( V_2 -V_3)^2}$$.
Question 2
1 / -0

An inductance and resistance are connected in series with an A.C circuit. In this circuit

A
the current and P.d. across the resistance lead P.d across the inductance by $$\dfrac{\pi }{2}$$

B
the current and P.d across the resistance lags behind the P.d. across the inductance by angle $$\dfrac{\pi }{2}$$

C
The current across resistance leads and the P.d across resistance lags behind the P.d across the inductance by $$\dfrac{\pi }{2}$$

D
the current across resistance lags behind and the P.d across the resistance leads the P.d across the inductance by $$\dfrac{\pi }{2}$$

Solution

This is very fundamental. If we apply separate voltages across resistance and inductor, then in resistance, current and voltage both are in same phase whereas in inductor, current across it lags p.d across it by $$\pi /2$$.
Now, when we apply voltage across inductor and resistance connencted in series then current through both of them will be same because of KCL. therefore voltage across resistor will be in same phase with current whereas voltage across inductor will lead the current across it by $$\pi /2$$. therefore current and voltage across resistor lags voltage across inductor by $$\pi /2$$.
Question 3
1 / -0

If a capacitor is connected to two different A.C. generators, then the value of capacitive reactance is:

A
directly proportional to frequency

B
inversely proportional to frequency

C
independent of frequency

D
inversely proportional to the square of frequency

Solution

$$X_C=\dfrac{1}{\omega c}$$

$$\therefore X_C \propto \dfrac{1}{\omega}$$
Question 4
1 / -0

A capacitor is connected to an A.C. circuit, then the phase difference between current and the voltage is :

A
$$\pi $$

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

C
$$\dfrac{-\pi }{2}$$

D
Zero

Solution

Current leads voltage by $$\dfrac{\pi}{2}$$

$$\therefore$$ phase difference is$$=\dfrac{\pi}{2}$$
Question 5
1 / -0

Ratio of impedance to capacitive reactance has

A
no units

B
ohm

C
ampere

D
tesla

Solution

$$Ratio=\dfrac{\omega L}{\dfrac{1}{wc}}$$

$$=w^2LC$$

$$WL \ and \ \dfrac{1}{wc}$$ has dimensions same as of resistance
Question 6
1 / -0

Statement ( A ) : The reactance offered by an inductance in A.C. circuit decreases with the increase of AC frequency.
Statement ( B ) : The reactance offered by a capacitor in AC circuit increases with the increase of AC frequency.

A
A is true but B is false

B
Both A and B are true

C
A is false but B is true

D
Both A and B are false

Solution

Reactance is independent of frequency.
Hence, both are false.
Question 7
1 / -0

A mixer of 100$$\Omega $$ resistance is connected to an A.C. source of 200V and 50 cycles/sec. The value of average potential difference across the mixer will be:

A
308 V

B
264 V

C
220 V

D
zero

Solution

We need to find the average potential difference across the mixer. Here by average we mean average over a long period of time. As we know in one complete cycle, average voltage across the mixer is zero. ( In one complete cycle current changes the direction and net voltage across a resistor is zero).
So when in one complete cycle voltage drop across the resistor is zero, then the average voltage drop across the resistor (mixer) is zero.
Question 8
1 / -0

Choose the wrong statement of the following :

A
The peak voltage across the inductor can be less than the peak voltage of the source in an LCR circuit

B
In a circuit containing and a capacitor and an ac source the current is zero at the instant source voltage is maximum

C
When an AC source is connected to a capacitor, then the rms current in the circuit gets increased if a dielectric slab is inserted into the capacitor

D
In a pure inductive circuit emf will be in phase with the current

Solution

In pure inductive circuit,
voltage leads by $$\dfrac{\pi}{2}$$.
Question 9
1 / -0

The equation of an alternating voltage is E=220 .Then the impedance of the circuit is:

A
10 ohm

B
22 ohm

C
11 ohm

D
17 ohm
Question 10
1 / -0

An inductor has a resistance $$R$$ and inductance $$L$$. It is connected to an AC source of emf $$E_{v}$$ and angular frequency $$\omega$$; then the current $$I_{v}$$ in the circuit is :

A
$$\dfrac{E_{v}}{\omega L}$$

B
$$\dfrac{E_{v}}{R}$$

C
$$\dfrac{E_{v}}{\sqrt{R^{2}+\omega ^{2}L^{2}}}$$

D
$$\sqrt{\left ( \dfrac{E_{v}}{R} \right )^{2}+\left ( \dfrac{E_{v}}{\omega L} \right )^{2}}$$

Solution

The impedance in R-L circuit is

$$\displaystyle Z=\sqrt{R^2+X_L^2}=\sqrt{R^2+(\omega L)^2}$$

The current, $$\displaystyle I_v=\dfrac{E_v}{Z}$$

$$=\dfrac{E_v}{\sqrt{R^2+(\omega L)^2}}$$

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Re-Attempt Weekly Quiz Competition

Alternating Current Test - 29

Result

Alternating Current Test - 29

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SHARING IS CARING

Question 1

$$V_{1}+V_{2}+V_{3}$$

$$\sqrt{V_{1}^{2}+(V_{2}+V_{3})^{2}}$$

$$V_{1}-V_{2}-V_{3}$$

$$\sqrt{V_{1}^{2}+(V_{2}-V_{3})^{2}}$$

Solution

Question 2

the current and P.d. across the resistance lead P.d across the inductance by $$\dfrac{\pi }{2}$$

the current and P.d across the resistance lags behind the P.d. across the inductance by angle $$\dfrac{\pi }{2}$$

The current across resistance leads and the P.d across resistance lags behind the P.d across the inductance by $$\dfrac{\pi }{2}$$

the current across resistance lags behind and the P.d across the resistance leads the P.d across the inductance by $$\dfrac{\pi }{2}$$

Solution

Question 3

directly proportional to frequency

inversely proportional to frequency

independent of frequency

inversely proportional to the square of frequency

Solution

Question 4

$$\pi $$

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

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

Zero

Solution

Question 5

no units

ohm

ampere

tesla

Solution

Question 6

A is true but B is false

Both A and B are true

A is false but B is true

Both A and B are false

Solution

Question 7

308 V

264 V

220 V

zero

Solution

Question 8

The peak voltage across the inductor can be less than the peak voltage of the source in an LCR circuit

In a circuit containing and a capacitor and an ac source the current is zero at the instant source voltage is maximum

When an AC source is connected to a capacitor, then the rms current in the circuit gets increased if a dielectric slab is inserted into the capacitor

In a pure inductive circuit emf will be in phase with the current

Solution

Question 9

10 ohm

22 ohm

11 ohm

17 ohm

Question 10

$$\dfrac{E_{v}}{\omega L}$$

$$\dfrac{E_{v}}{R}$$

$$\dfrac{E_{v}}{\sqrt{R^{2}+\omega ^{2}L^{2}}}$$

$$\sqrt{\left ( \dfrac{E_{v}}{R} \right )^{2}+\left ( \dfrac{E_{v}}{\omega L} \right )^{2}}$$

Solution

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