An electric circuit containing an inductance L and resistance R in series has an impedance of 50 Ω at 100 H z and an impedance of 100 Ω at 500 H z . Find the values of L and R .

Given, Net impedance of the circuit Z 1 = 50 Ω at f 1 = 100 H z And net impedance Z 2 = 100 Ω at f 2 = 500 H z Impedance, Z = R 2 + 4 π 2 f 2 L 2 ⇒ 50 = R 2 + 4 π 2 100 2 L 2 or R 2 + 4 π 2 100 2 L 2 = 2500 …(i) Similarly, 100 = R 2 + 4 π 2 500 2 L 2 or R 2 + 4 π 2 500 2 L 2 = 10000 …(ii) Solving equations (i) and (ii), we get L = 28.13 × 10 - 3 H and R = 46.77 Ω .

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Calculate the impedance and the rms current in the a.c. circuit shown in figure.

Important Questions on Alternating Current and Electrical Machines

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 9

The virtual current in the a.c. circuit shown in Figure, is $1.0 A$ . Find (i) virtual voltage across the coil $L$ (ii) impedance of the circuit and (iii) reactance of the coil.

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 10

A circuit containing a resistance of

50 Ω

and an inductance of

(1 / π)

H in series is connected to a

200 V

a.c. line of frequency

60 H z

. Find the reactance, the impedance, the current in the circuit and the phase difference between the alternating voltage and current.

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 11

An a.c. circuit consists of a

220 V,

50 H z

supply connected across a

100 Ω

resistor. What inductance should be connected in the circuit in series with resistance so that the current is reduced to half?

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 12

A long solenoid connected to a

12 V

d.c. source passes a steady current of

2 A .

When the solenoid is connected to an a.c. source of

12 V

50 H z

, the current flowing is

1 A

. Calculate the inductance of the solenoid.

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 13

A choke coil and a resistance are connected in series in an a.c. circuit. A potential difference of

130 V

is applied to the circuit. If the potential difference across the resistance is

50 V

, what should be the potential difference across the choke coil?

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PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 14

An emf,

ε = 200 \sin 377 t

volt is applied across an inductance

L

having a resistance of

1.0 Ω

. The maximum current is found to be

10 A

. Find the value of

L

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IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 15

An electric circuit containing an inductance

L

and resistance

R

in series has an impedance of

50 Ω

100 H z

and an impedance of

100 Ω

500 H z

. Find the values of

L

and

R

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IMPORTANT

PHYSICS A Reference Book for Class 12 Volume 2>Chapter 1 - Alternating Current and Electrical Machines>Problems For Practice>Q 16

In the RL-circuit shown in figure, resistance

R = 30 Ω

, reactance

X_{L} = 40 Ω

and peak emf

= 220 V

.
Calculate the (i) impedance

Z .

(ii) phase difference between the emf and current and (iii) the peak current

I_{0}

in the circuit.

Calculate the impedance and the rms current in the a.c. circuit shown in figure.

Important Questions on Alternating Current and Electrical Machines

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