# The peak value of an alternating e.m.f. E is given by $E={E}_{0}\mathrm{cos}\omega \text{\hspace{0.17em}}t$ is 10 volts and its frequency is 50 Hz. At time $t=\frac{1}{600}sec$, the instantaneous e.m.f. is (1) 10 V (2) $5\sqrt{3}\text{\hspace{0.17em}}V$ (3) 5 V (4) 1 V

Subtopic:  Different Types of AC Circuits |
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If a current I given by ${I}_{0}\mathrm{sin}\text{\hspace{0.17em}}\left(\omega \text{\hspace{0.17em}}t-\frac{\pi }{2}\right)$ flows in an ac circuit across which an ac potential of $E={E}_{0}\mathrm{sin}\omega \text{\hspace{0.17em}}t$ has been applied, then the power consumption P in the circuit will be

(1) $P=\frac{{E}_{0}{I}_{0}}{\sqrt{2}}$

(2) $P=\sqrt{2}{E}_{0}{I}_{0}$

(3) $P=\frac{{E}_{0}{I}_{0}}{2}$

(4) P = 0

Subtopic:  Different Types of AC Circuits |
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A resistance of 20 ohms is connected to a source of an alternating potential, V = 220sin(100πt). The time taken by the current to change from its peak value to its r.m.s value will be:

1. 0.2 sec

2. 0.25 sec

3. 25 × 10–3 sec

4. 2.5 × 10–3 sec

Subtopic:  RMS & Average Values |
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An alternating current of frequency ‘f’ is flowing in a circuit containing a resistance R and a choke L in series. The impedance of this circuit will be:

1. R + 2πfL

2. $\sqrt{{R}^{2}+4{\pi }^{2}{f}^{2}{L}^{2}}$

3. $\sqrt{{R}^{2}+{L}^{2}}$

4. $\sqrt{{R}^{2}+2\pi fL}$

Subtopic:  Different Types of AC Circuits |
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A resistance of 300 Ω and an inductance of $\frac{1}{\pi }$ henry are connected in series to an ac voltage of 20 volts and a 200 Hz frequency. The phase angle between the voltage and current will be:

1. ${\mathrm{tan}}^{-1}\frac{4}{3}$

2. ${\mathrm{tan}}^{-1}\frac{3}{4}$

3. ${\mathrm{tan}}^{-1}\frac{3}{2}$

4. ${\mathrm{tan}}^{-1}\frac{2}{5}$

Subtopic:  Different Types of AC Circuits |
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In a region of uniform magnetic induction B = 10–2 tesla, a circular coil of radius 30 cm and resistance π2 ohm is rotated about an axis that is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is :

(1) 4π2 mA

(2) 30 mA

(3) 6 mA

(4) 200 mA

Subtopic:  Different Types of AC Circuits |
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In a LCR circuit having L = 8.0 henry, C = 0.5 μF and R = 100 ohm in series. The resonance frequency in radian per second is

(2) 600 Hz

(4) 500 Hz

Subtopic:  Different Types of AC Circuits |
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The impedance of a circuit consists of 3 ohm resistance and 4 ohm reactance. The power factor of the circuit is :

(1) 0.4

(2) 0.6

(3) 0.8

(4) 1.0

Subtopic:  Different Types of AC Circuits |
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The power factor of a good choke coil is:

(1) Nearly zero

(2) Exactly zero

(3) Nearly one

(4) Exactly one

Subtopic:  Different Types of AC Circuits |
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L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representing the dimension of frequency will be:

1. LC

2. (LC)–1/2

3. ${\left(\frac{L}{C}\right)}^{-1/2}$

4. $\frac{C}{L}$

Subtopic:  Different Types of AC Circuits |
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