What is an alternating current? Prove the following for a.c (ii) I a v g = 2 I 0 π for the positive half cycle.

Alternating current: Alternating current is an electric current that periodically reverses its direction and changes magnitude continuously with respect to time. The average value of the a.c over half positive cycle: I a v g T 2 = ∫ 0 T 2 I d t ∫ 0 T 2 d t I a v g T 2 = 2 T ∫ 0 T 2 I 0 sin w t + ϕ d t = 2 I 0 T - cos w t + ϕ w 0 T 2 = 2 I 0 T w - cos w t 2 + ϕ + cos ϕ = 2 I 0 2 π - cos π + ϕ + cos ϕ = I 0 π cos ϕ + cos ϕ I a v g T 2 = 2 I 0 cos ϕ π So, the maximum value of average value of the current in the half positive cycle is I a v g = 2 I 0 π

E M B I B E

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 18

EASY

12th Odisha Board

IMPORTANT

Earn 100

Graphically show the variation of inductive reactance and capacitive reactance with the frequency of AC.

Important Questions on Alternating Currents

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12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 1

Which of the following effects is not possible by A.C?

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 2

AC ammeters actually measure _____.

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 3

If

R, Z, R_{L}

and

R_{C}

stand for resistance, impedance, inductive reactance and capacitive reactance of an AC circuit respectively, then the power factor of an AC circuit is given by _____.

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12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 4

The emf of an AC circuit is given by

e = 60 \sin (53.141 t)

and the current by

i = \frac{(60)}{10.628} \sin (53.141 t - \frac{π}{2}) .

Then the power consumed by the circuit is _____.

EASY

12th Odisha Board

IMPORTANT

Bureau's Higher Secondary Physics Class 12>Chapter 10 - Alternating Currents>MODEL QUESTIONS>Q 5

The peak values of emf and current of an AC circuit containing R, L and C where inductance and capacitance are equal are obtained as $200 V$ and $20 A$ respectively. The average power of the circuit is _____.