A resistor, a capacitor and an inductor ( R = 300 Ω , C = 20 μF , L = 1 . 0 Henry ) are connected in series with an AC source of, E rms = 50 V and v = 50 π Hz . Find (a) the rms current in the circuit and (b) the rms potential differences across the capacitor, the resistor and the inductor.

Given that Resistor R = 300 Ω Capacitor C = 20 μF Inductor L = 1 . 0 henry AC source voltage and frequency E rms = 50 V and ν = f = 50 π Hz . The reactance of the circuit X L = 2 π f L = 2 π 50 π 1 = 100 Ω and X C = 1 2 π f C = 1 2 π 50 π 20 × 10 - 6 = 500 Ω The total reactance of the circuit The reactance of the circuit X = X C – X L = 500 - 100 = 400 Ω Since X L < X C , the circuit is called capacitive Impedance of the circuit Z = R 2 + x 2 = 300 2 + 400 2 = 500 Ω The current i r m s = V r m s Z = 50 500 = 0 . 1 A b The rms potential differences across the capacitor V C = i r m s x C = 0 . 1 × 500 = 50 V The rms potential differences across the resistor V L = i r m s x L = 0 . 1 × 100 = 10 V The rms potential differences across the inductor. V R = i r m s R = 0 . 1 × 300 = 30 V (Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source.)

A coil draws a current of 1 . 0 ampere and a power of 100 watt from an A.C. source of 110 volt and 5 22 π Hz . Find the inductance and resistance of the coil.

Given that, Rating of coil, i rms = 1 . 0 A and P = 100 watt . Voltage and frequency of AC mains V rms = 110 volts and f = 5 π 22 Hz Total power is consumed by resistance, so we assume lamp as a resistance for dc circuit. The resistance of the coil P = i 2 R ⇒ 100 = 1 R ⇒ R = 100 Ω For AC circuit Impedance of the circuit i rms = V rms Z ; here i rms = 1 . 0 A and V rms = 110 V So, Z = V rms i rms = 110 1 = 110 Ω (i) For inductance of the inductor, From Z 2 = R 2 + x 2 ⇒ x 2 = Z 2 - R 2 ⇒ x 2 = 110 2 - 100 2 ⇒ x = 10 21 Ω For inductance of the inductor x = 2 π f L ⇒ 10 21 = 2 π 5 22 π L ⇒ L = 21 22 H

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An electric bulb is designed to consume $55 W$ when operated at $110 volts$ . It is connected to a $220 V$ , $50 Hz$ line through a choke coil in series. What should be the inductance of the coil for which the bulb gets the correct voltage?

Important Questions on Alternating Current

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 10

A resistor, a capacitor and an inductor

(R = 300 Ω, C = 20 μF, L = 1.0 Henry)

are connected in series with an AC source of,

E_{rms} = 50 V

and

v = \frac{50}{π} Hz .

Find (a) the rms current in the circuit and (b) the rms potential differences across the capacitor, the resistor and the inductor.

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 11

In a series LCR circuit with a source of $50 V, R = 300 Ω$ , frequency $v = \frac{50}{π} Hz$ . The average electric field energy stored in the capacitor and average magnetic field energy stored in the coil are $25 mJ$ and $5 mJ$ respectively. The RMS current in the circuit is $0.10 A$ . Then find:

(a) Capacitance $(C)$ of capacitor

(b) Inductance $(L)$ of inductor.

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 12

A $20 volts, 5 watt$ lamp (lamp to be treated as a resistor) is used on AC mains of $200 volts$ and $\frac{50}{π} \sqrt{11}$ c.p.s. Calculate the

(i) capacitance of the capacitor, or inductance of the inductor, to be put in series to run the lamp.

(ii) How much pure resistance should be included in place of the above device so that the lamp can run on its rated voltage.

(iii) which is more economical (the capacitor, the inductor or the resistor).

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 13

A circuit has a resistance of $50 ohms$ and an inductance of $\frac{3}{π}$ henry. It is connected in series with a condenser of $\frac{40}{π} μF$ and AC supply voltage of $200 V$ and $50 cycles per \sec .$ Calculate

(i) the impedance of the circuit,

(ii) the p.d. across inductor coil and condenser.

(iii) Power factor

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 14

A coil draws a current of

1.0 ampere

and a power of

100 watt

from an A.C. source of

110 volt

and

\frac{5 \sqrt{22}}{π} Hz

. Find the inductance and resistance of the coil.

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 15

An inductor $\frac{2}{π}$ Henry, a capacitor $\frac{100}{π} μF$ and a resistor $75 Ω$ are connected in series across a source of emf $V = 10 \sin 100 π t .$ Here $t$ is in second.

(a) Find the impedance of the circuit.

(b) Find the energy dissipated in the circuit in $20$ minutes.

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 16

A series circuit consists of resistance, inductance and capacitance. The applied voltage and the current at any instant are given by

$E = 141.4 \cos (5000 t - 10 º) V$

and $I = 5 \cos (5000 t - 370 º) A$

The inductance is $0.01 H$ . Calculate the value of capacitance and resistance.

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Alpha Question Bank for Engineering: Physics>Chapter 28 - Alternating Current>Exercise - 1>Q 17

The inductance of

2.0 H

, the capacitance of

18 μF

and the resistance

10 kΩ

is connected to an AC source of

20 V

with adjustable frequency.

(a)

What frequency should be chosen to maximize the current in the circuit?

(b)

What is the value of this maximum current?

An electric bulb is designed to consume 55 W when operated at 110 volts. It is connected to a 220 V, 50 Hz line through a choke coil in series. What should be the inductance of the coil for which the bulb gets the correct voltage?

Important Questions on Alternating Current

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An electric bulb is designed to consume $55 W$ when operated at $110 volts$ . It is connected to a $220 V$ , $50 Hz$ line through a choke coil in series. What should be the inductance of the coil for which the bulb gets the correct voltage?