A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied emf by a phase angle of π 2 . What is inductive reactance? Draw a graph showing the variation of inductive reactance with frequency of an a.c. source.

Let a pure inductor L is connected across an a.c. source and inductive reactance X L . Emf of alternating E = E o S i n ω t . Emf induced in inductor d i d t = V L , ⇒ d i = V L d t = V o S i n ω t L d t Integrating both side ∫ d i = ∫ V o S i n ω t L d t ⇒ i = - V m ω L C o s ω t ∴ i = - V m ω L C o s ω t = - V m ω L S i n ω t + π 2 ∴ i = i m sin ω t + π 2 , where i m = V m ω L which is equivalent to i = V X L . ∴ X L = ω L , ϕ = π 2 .

A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied emf by a phase angle of π 2 . What is inductive reactance? Draw a graph showing the variation of inductive reactance with frequency of an a.c. source.

Let a pure inductor L is connected across an a.c. source and inductive reactance X L . Emf of alternating E = E o S i n ω t . Emf induced in inductor d i d t = V L , ⇒ d i = V L d t = V o S i n ω t L d t Integrating both side ∫ d i = ∫ V o S i n ω t L d t ⇒ i = - V m ω L C o s ω t ∴ i = - V m ω L C o s ω t = - V m ω L S i n ω t + π 2 ∴ i = i m sin ω t + π 2 , where i m = V m ω L which is equivalent to i = V X L . ∴ X L = ω L , ϕ = π 2 .

An alternating emf is applied across a capacitor. Show mathematically that the current in it leads the applied emf by a phase angle of π 2 . What is capacitive reactance of such a circuit. Draw a graph showing the variation of capacitive reactance with the frequency of the ac current.

Let potential drop across the plate of capacitor V = Q C . Where C is capacitance of capacitor and q is charge stored. Voltage applied to circuit is E = E o S i n ω t . Potential difference in the circuit is must be equal to applied voltage V = Q C = E o S i n ω t For instantaneous current i = d Q d t = d C E o sin ω t d t = C E o ω C o s ω t ∴ i = E o 1 ω C sin ω t + π 2 ∵ sin 90 + θ = cos θ For maximum current sin ω t + π 2 = 1 , ∴ I o = E o 1 ω C . Compare with I = I o sin ω t + π 2 We get phase π 2 .

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12th West Bengal Board

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A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied emf by a phase angle of $\frac{π}{2} .$ What is inductive reactance? Draw a graph showing the variation of inductive reactance with frequency of an a.c. source.

Important Questions on Transient Current and Alternating Current

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 18

An alternating emf is applied across a capacitor. Show mathematically that the current in it leads the applied emf by a phase angle of

\frac{π}{2} .

What is capacitive reactance of such a circuit. Draw a graph showing the variation of capacitive reactance with the frequency of the ac current.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 19

Draw a labelled diagram of an ac generator. Write the principle on which it works.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 20

With the help of a labelled diagram, explain the working principle of step-up transformer.

MEDIUM

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 21

Obtain the relation

O = I_{0} \sin (ωt + π / 2)

and

X_{C} = 1 / ωC

for a pure capacitor across which an alternating emf

V = V_{0}

\sin ω t

is applied. Draw a phasor diagram showing emf

V

, current

I

and their phase difference

ϕ

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 22

What are free

L - C

oscillations? Discuss qualitatively how are they produced. Show that their angular frequency is

\frac{1}{\sqrt{L C}}

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 23

A charged capacitor is connected across an inductor with a wire having practically no resistance. Show that the discharge of the capacitor is oscillatory. Find the frequency of oscillations.

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 24

Derive an expression for the average power consumed in a series LCR circuit connected to ac source in which the phase-difference between the voltage and current in the circuit is $ϕ$

HARD

12th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART 2 : CLASS 12>Chapter 10 - Transient Current and Alternating Current>EXERCISE 10>Q 24

Define the quality factor in an ac circuit. Why should the quality factor have high value in receiving circuits. Name the factors on which it depends.

A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied emf by a phase angle of π2. What is inductive reactance? Draw a graph showing the variation of inductive reactance with frequency of an a.c. source.

Important Questions on Transient Current and Alternating Current

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A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied emf by a phase angle of $\frac{π}{2} .$ What is inductive reactance? Draw a graph showing the variation of inductive reactance with frequency of an a.c. source.