Show that the average power dissipated per cycle in an L - C - R circuit is given by P = V rms × I rms × cos ϕ , where ϕ is the angle of lag or lead.

power in L-C-R circuit : P = V ⋅ I = V 0 sinωt . I 0 sin ωt - ϕ = V 0 I 0 sinωt . sin ωt - ϕ = V 0 I 0 ⋅ 1 2 [ cosϕ − sin 2 ωt ] sin 2 ωt have average value of = 0 on a cycle.So, P = V 0 I 0 2 cosϕ P = V rms I rms ⋅ cosϕ Where , ϕ = phase angle cosϕ = power factor

EASY

12th ICSE

IMPORTANT

Earn 100

An $AC$ emf $V - V_{0} \sin ωt$ is applied across a pure inductance $L$ . Obtain expressions for (ii) the inductive reactance $X_{L}$ in the circuit. Draw a phasor diagram showing emf $V_{0}$ , current $I_{0}$ and their phase difference $ϕ$ .

Important Questions on Alternating Current

HARD

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 7

Explain the meaning of ‘reactance’. Derive expression for the reactance of an inductor

L

connected across an

AC

source. Give its unit. Show that no power is dissipated in an inductor when

AC

passes through it.

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 8

Obtain the relation for the current

I = I_{0} \sin (ωt - π / 2)

for a pure inductor across which an alternating emf

V = V_{0}

sin cot is applied.

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 9

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

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 10

A capacitor

C

is connected to an

AC

voltage source

V = V_{0} \sin ω t

. Draw a circuit diagram for it. Obtain an expression for the current / flowing in the circuit. Express it as a sin function. What is the phase difference between current

I

and voltage

V

? What is the reactance of the capacitor?

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 11

What is impedance of an

AC

circuit? A capacitor

C

and a resistor

R

are connected in series in an

AC

circuit. Derive expression for the impedance

Z

of the circuit. Draw phasor diagram.

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 12

In an alternating-current circuit an inductance

L

, a capacitance

C

and a resistance

R

are connected in series. Derive expression for the impedance and the phase angle. What is the impedance at resonance?

MEDIUM

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 13

Derive an expression for the phase angle of an

AC

circuit with an inductor

L

, a capacitor

C

and a resistor

R

in series. Draw the phasor diagram if the voltage across the capacitor is greater than that across the inductor. Obtain an expression for the resonant frequency of the circuit.

EASY

12th ICSE

IMPORTANT

NOOTAN ISC PHYSICS Class 12 Part-1>Chapter 12 - Alternating Current>QUESTIONS>Q 14

Show that the average power dissipated per cycle in an

L - C - R

circuit is given by

P = V_{rms} \times I_{rms} \times \cos ϕ

, where

ϕ

is the angle of lag or lead.

An AC emf V-V0 sin ωt is applied across a pure inductance L. Obtain expressions for (ii) the inductive reactance XL in the circuit. Draw a phasor diagram showing emf V0, current I0 and their phase difference ϕ.

Important Questions on Alternating Current

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An $AC$ emf $V - V_{0} \sin ωt$ is applied across a pure inductance $L$ . Obtain expressions for (ii) the inductive reactance $X_{L}$ in the circuit. Draw a phasor diagram showing emf $V_{0}$ , current $I_{0}$ and their phase difference $ϕ$ .