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

Show that the average power dissipated in an AC circuit is, in general, given by P = V rms × I rms × R / Z where R is the resistance of the circuit (defined as real part of the complex impedance) and Z is the impedance.

Power, P = v rms ⋅ I rms ⋅ cosϕ the, cosϕ = power factor cosϕ = R Z So, P = V rms I rms ⋅ R Z

E M B I B E

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

MEDIUM

12th ICSE

IMPORTANT

Earn 100

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?

Important Questions on Alternating Current

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