Alternating Current Test

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Alternating Current Test - 78

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Question 1
1 / -0

In the given AC circuit

A
current $I_2$ and V are is same phase

B
current $I_2$ leads $I_1$ by $90^0$

C
current I leads $I_2$ by $\theta < 90^0$

D
current I leads $I_1$ by $\theta < 90^0$

Solution
Question 2
1 / -0

An alternating current of $1.5mA$ and angular frequency $300\ rad/sec$ flows through a $10K\Omega$ resistor and a $0.50\mu F$ capacitor in series. find the rms voltage across the capacitor and impedance of the circuit?

A
$1.2\times 10^{4}\Omega ;\ 10V$

B
$10^{4}\Omega ;\ 10^{4}V$

C
$1.0\times 1.0^{4}\Omega ;\ 50V$

D
$10\Omega ;10v$

Solution

$V_{rms}$ across capacitor $=I_{rms} \times C$
$=1.5 \times 10^{-3} \times \cfrac 1 {\omega C}$
$=1.5\times 10^{ -3 }\times \cfrac { 1 }{ 300\times 0.5\times { 10 }^{ -6 } }$
$=1 \times 10$
$10 V$
Impedance of circuit is
$Z=\sqrt { { R }^{ 2 }+{ X }_{ C }^{ 2 } }$
$=\sqrt { ({ 10\times { 10 }^{ 3 }) }^{ 2 }+({ \cfrac { 1 }{ 1.5\times { 10 }^{ -4 } } ) }^{ 2 } }$
$=\sqrt { { 10 }^{ 8 }+\cfrac { { 10 }^{ 8 } }{ ({ 1.5) }^{ 2 } } }$
$=1.2 \times 10^4 \quad\Omega$
Question 3
1 / -0

An inductance of $2H$ , capacitance of $8\mu F$ and resistance of $10K\Omega$ are connected in series to an AC source of $100V$ with adjustable frequency. The angular frequency at which current in the circuit is maximum is :

A
$50 \ rad/s$

B
$100 \ rad/s$

C
$125 \pi \ rad/s$

D
$250 \ rad/s$

Solution
Question 4
1 / -0

A bulb is rated $55 W/110 V$ . It is to be connected to a $220 V/50 Hz$ with inductor in series. The value inductance, so that bulb gets correct voltage is:

A
$220 \omega^{-1}$

B
$110 \omega^{-1}$

C
$377.5 \omega^{-1}$

D
$300 \omega^{-1}$

Solution
Question 5
1 / -0

If ${W_1}and\;{W_2}$ are half power frequencies of series LCR circuit, Then the reasonant frequency of the circuit is-

A
$\sqrt {{W_1}\;{W_2}}$

B
$\frac{{{W_1} + {W_2}}}{2}$

C
$\sqrt {\frac{{{W_1} + {W_2}}}{2}}$

D
$\frac{{{W_1} -{W_2}}}{2}$

Solution
Question 6
1 / -0

In an a.c. circuit consisting of resistance $R$ and inductance $L$ , the voltage across $R$ is $60$ volt and that across $L$ is $80$ Volt.The total Voltage across the combination is

A
$140 V$

B
$20 V$

C
$100 V$

D
$70 V$

Solution
Question 7
1 / -0

If alternating current of rms value 'a' flows through resistance R then power loss in resistance is :

A
Zero

B
$a^2R$

C
$\dfrac{a^2R}{2}$

D
$2 a^2R$

Solution

[B] $P = {I^2}_{RMS}R$
$= {a^2}R$
Question 8
1 / -0

An oscillating circuit of a capacitor with capacitance $C$ , a coil of inductance $L$ with negligible resistance, and switch. With the switch disconnected the capacitor was charged to a voltage $V_m$ and then at the moment $t=0$ , the switch was closed. The current $I$ in the circuit as a function of time is represented as

A
$V_m\sqrt{\frac{L}{C}} sin (wt)$

B
$V_m\sqrt{\frac{C}{L}} sin (wt)$

C
$V_m\sqrt{\frac{L}{C}} cos (wt)$

D
$V_m\sqrt{\frac{C}{L}} sin (wt)$

Solution
Question 9
1 / -0

The inductive reactance of a coil is $1000\Omega .$ If its self inductance and frequency both are increased two times, then inductive reactance will be

A
$1000 \Omega$

B
$2000 \Omega$

C
$4000 \Omega$

D
$16000 \Omega$

Solution
Question 10
1 / -0

Calculate the capacitive reactance of a condenser in order to run a bulb rated at $10\ watt\ 60\ volt$ when connected in series to an a.c. source of $100\ volt$ .

A
$100\Omega$

B
$360\Omega$

C
$600\Omega$

D
$480\Omega$

Solution

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Re-Attempt Weekly Quiz Competition

Alternating Current Test - 78

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Alternating Current Test - 78

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Question 1

current I2I_2I2​ and V are is same phase

current I2I_2I2​ leads I1I_1I1​ by 90090^0900

current I leads I2I_2I2​ by θ<900\theta < 90^0θ<900

current I leads I1I_1I1​ by θ<900\theta < 90^0θ<900

Solution

Question 2

1.2×104Ω; 10V1.2\times 10^{4}\Omega ;\ 10V1.2×104Ω; 10V

104Ω; 104V10^{4}\Omega ;\ 10^{4}V104Ω; 104V

1.0×1.04Ω; 50V1.0\times 1.0^{4}\Omega ;\ 50V1.0×1.04Ω; 50V

10Ω;10v10\Omega ;10v10Ω;10v

Solution

Question 3

50 rad/s50 \ rad/s50 rad/s

100 rad/s100 \ rad/s100 rad/s

125π rad/s125 \pi \ rad/s125π rad/s

250 rad/s250 \ rad/s250 rad/s

Solution

Question 4

220ω−1220 \omega^{-1}220ω−1

110ω−1110 \omega^{-1}110ω−1

377.5ω−1377.5 \omega^{-1}377.5ω−1

300ω−1300 \omega^{-1}300ω−1

Solution

Question 5

W1 W2\sqrt {{W_1}\;{W_2}} W1​W2​​

W1+W22\frac{{{W_1} + {W_2}}}{2}2W1​+W2​​

W1+W22\sqrt {\frac{{{W_1} + {W_2}}}{2}} 2W1​+W2​​​

W1−W22\frac{{{W_1} -{W_2}}}{2}2W1​−W2​​

Solution

Question 6

140V140 V140V

20V20 V20V

100V100 V100V

70V70 V70V

Solution

Question 7

Zero

a2Ra^2Ra2R

a2R2\dfrac{a^2R}{2}2a2R​

2a2R2 a^2R2a2R

Solution

Question 8

VmLCsin(wt)V_m\sqrt{\frac{L}{C}} sin (wt)Vm​CL​​sin(wt)

VmCLsin(wt)V_m\sqrt{\frac{C}{L}} sin (wt)Vm​LC​​sin(wt)

VmLCcos(wt)V_m\sqrt{\frac{L}{C}} cos (wt)Vm​CL​​cos(wt)

VmCLsin(wt)V_m\sqrt{\frac{C}{L}} sin (wt)Vm​LC​​sin(wt)

Solution

Question 9

1000Ω1000 \Omega1000Ω

2000Ω2000 \Omega2000Ω

4000Ω4000 \Omega4000Ω

16000Ω16000 \Omega16000Ω

Solution

Question 10

100Ω100\Omega100Ω

360Ω360\Omega360Ω

600Ω600\Omega600Ω

480Ω480\Omega480Ω

Solution

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current $I_2$ and V are is same phase

current $I_2$ leads $I_1$ by $90^0$

current I leads $I_2$ by $\theta < 90^0$

current I leads $I_1$ by $\theta < 90^0$

$1.2\times 10^{4}\Omega ;\ 10V$

$10^{4}\Omega ;\ 10^{4}V$

$1.0\times 1.0^{4}\Omega ;\ 50V$

$10\Omega ;10v$

$50 \ rad/s$

$100 \ rad/s$

$125 \pi \ rad/s$

$250 \ rad/s$

$220 \omega^{-1}$

$110 \omega^{-1}$

$377.5 \omega^{-1}$

$300 \omega^{-1}$

$\sqrt {{W_1}\;{W_2}}$

$\frac{{{W_1} + {W_2}}}{2}$

$\sqrt {\frac{{{W_1} + {W_2}}}{2}}$

$\frac{{{W_1} -{W_2}}}{2}$

$140 V$

$20 V$

$100 V$

$70 V$

$a^2R$

$\dfrac{a^2R}{2}$

$2 a^2R$

$V_m\sqrt{\frac{L}{C}} sin (wt)$

$V_m\sqrt{\frac{C}{L}} sin (wt)$

$V_m\sqrt{\frac{L}{C}} cos (wt)$

$V_m\sqrt{\frac{C}{L}} sin (wt)$

$1000 \Omega$

$2000 \Omega$

$4000 \Omega$

$16000 \Omega$

$100\Omega$

$360\Omega$

$600\Omega$

$480\Omega$