(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage? (ii) Without making any other change, find the value of the additional capacitor C 1 , to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

Given, Inductance of the circuit L = 100 m H Capacitance of the circuit C = 2 μ F Resistance of the circuit R = 400 Ω Voltage of the source V = V 0 sin 1000 t + ϕ So, angular frequency, ω = 1000 r a d s - 1 . Inductive reactance X L = ω L = 1000 × 100 × 10 - 3 Ω = 100 Ω . Capacitive reactance X C = 1 ω C = 1 1000 × 2 × 10 - 6 Ω = 500 Ω . (i) Phase value ϕ between current and voltage is given by, tan ⁡ ϕ = X L - X C R = 100 - 500 400 = - 1 ⇒ ϕ = - π 4 ϕ is negative, implies X L > X C or the current leads the voltage by π / 4 rad. (ii) Power factor is unity when X C = X L or 1 ω C ' = 100 Ω ⇒ C ' = 1 100 ω = 1 100 × 1000 F = 10 μ F ⇒ C ' = C + C 1 or 10 = 2 + C 1 ∴ Required capacitance need to be added C 1 = 8 μ F .

Describe the ways in which Eddy currents are used to advantage.

When bulk pieces of conductors are subjected to changing magnetic flux, induced currents produced in them are called eddy currents. The eddy currents can be used to advantage in the following ways: (i) Magnetic braking in trains: Strong electromagnets are situated above the rails in electrically powered trains. When electromagnets are activated, the eddy currents induced in the rails oppose the motion of the train. As there are no mechanical linkages, the braking effect is smooth. (ii) Electromagnetic damping: Moving coil galvanometers have a fixed core made of nonmagnetic metallic material. When the coil oscillates, the eddy currents generated in the core oppose the motion and bring the coil to rest quickly. (iii) Induction furnace: It can be used to produce high temperatures and can be utilised to prepare alloys by melting the constituent metals. A high frequency alternating current is passed through a coil which surrounds the metal to be melted. The eddy currents generated in the metals produce high temperatures sufficient to melt. (iv) Electric power meters: A metal disc is present inside it. Electric currents are induced in it, and it rotates in a magnetic field induced by the alternating current in the coil.

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Earn 100

Derive expression for energy stored in an inductor.

Important Questions on Electromagnetic Induction and Alternating Current

MEDIUM

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 114

With the help of phasor diagram, find the expression for the impedances of an

L - C - R

circuit.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 115

Find average value of ac current in its first positive half cycle.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 116

An inductor

200 m H

, capacitor

500 μ F

, resistor

10 Ω

are connected in series with a

100 V

, variable frequency a.c. source. Calculate the (i) frequency at which the power factor of the circuit is unity, (ii) current amplitude at this frequency, (iii) Q-factor.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 117

An LCR-series circuit with

L = 100 m H, C = 100 μ F, R = 120 Ω

is connected to an a.c. source of emf

ε = 30 \sin 100 t

volt. Find the impedance, peak current and resonant frequency of the circuit.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 118

(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage?

Question Image

(ii) Without making any other change, find the value of the additional capacitor $C_{1}$ , to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 119

40 Ω

resistor,

3 m H

inductor and

2 μ F

capacitor are connected in series to a

110 V, 5000 H z

a.c. source. Calculate the value of the current in the circuit

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 120

A capacitor of unknown capacitance, a resistance of

100 Ω

and an inductor of self-inductance

L (= 4 / π^{2})

henry are connected in series across an a.c. source of

200 V

and

50 H z

. Calculate the value of the capacitance and the current that flows in the circuit when the current is in phase with the voltage.

HARD

12th Tamil Nadu Board

IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 4 - Electromagnetic Induction and Alternating Current>Exercise>Q 121

50 μ F

capacitor,

0.05 H

inductor and a

48 Ω

resistor are connected in series with an a.c. source of emf,

ε = 310 \sin 314 t

.Calculate the reactance of circuit and tell its nature. What is the phase angle between the current and the applied emf?

Derive expression for energy stored in an inductor.

Important Questions on Electromagnetic Induction and Alternating Current

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