Alternating Current Test

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Alternating Current Test - 78

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Question 1
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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