Deduce an equation U = 1 2 L I 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power, rate of doing work ). = ε I dt (power = voltage (emf) x current). But ε = - L di dt (in case of an inductor). therefor dw = LI dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Deduce an equation U = 1 2 L I 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power, rate of doing work ). = ε I dt (power = voltage (emf) x current). But ε = - L di dt (in case of an inductor). therefor dw = LI dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

Using the equation di dt + R L i + 1 LC ∫ idt = V m L e iωt . for L-C-R circuit, obtain an equation for the complex current ' i ' and explain its different terms in the equation. Hence obtain the equation for real current ' i '

The given equation is di dt + R L i + 1 LC ∫ idt = V m L e iωt This equation can be written as by multiplying by LI R as, Li di dt + Ri 2 + q C i = v i Explanation of different terms: Since Li di dt = d dt 1 2 Li 2 . =The rate of change of energy stored in an inductor. Ri 2 = joule heating loss. q c i = d dt q 2 2 C =rate of change of energy stored in the capacitor. v i = p o w e r rate at which driving force pours in energy. It goes into (i) ohmic loss and (ii) increase of stored energy. The equation can be written as L d 2 q dt 2 + R dq dt + q C = E 0 sinωt . This is like an equation of a forced oscillator.. Its solution is, q = q o sin ωt + θ so dq dt = q o ωcos ωt + θ and d 2 q dt 2 = - q o ω 2 sin ωt + θ The current in the circuit is given by, I = dq dt = q o ωcos ωt + ϕ = q o ωcos ωt + ϕ - π 2 , Where π 2 is the phase difference Therefore we can write, I = I 0 sin ( ω t + ϕ ) . This is the required euation.

Deduce an equation U = 1 2 LI 2 for an inductor.

Energy stored in an inductor is work done in increasing the current from zero to certain value. Let dw be the small work done during a small interval of time dt so dw = P . dt ( P = power , rate of doing work) = ε I dt ( power = voltage (emf) x current ) But ε = - L di dt ( in case of an inductor) therefor dw = L dI dt dt = LIdI Total work done in increasing the current from zero to a value I ∫ 0 t dw = ∫ 0 i LidI = L ∫ 0 i idI = 1 2 LI 2 This is the required expression

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 9

EASY

12th Gujarat Board

IMPORTANT

Earn 100

In AC generator, induced emf is zero at time $t = 0$ . The induced emf at time $\frac{π}{w}$ is _____.

50% studentsanswered this correctly

Important Questions on Alternating Current

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 10

In an L-C oscillator circuit having a completely charged capacitor, with the passage of time _____.

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 11

Deduce an equation

U = \frac{1}{2} L I^{2}

for an inductor.

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 12

Using

P = V_{r m s} I_{r m s} \cos δ

, discuss any two special cases for power consumed in an AC circuit.

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 13

In an ideal step-up transformer input voltage is

110 V

and current flowing in the secondary is

10 A

. If the transmission ratio is

10

then calculate output voltage and current in primary.

HARD

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2019>Q 14

Write the differential equation for charge in L-C-R series A.C. circuit and obtain an equation for complex current from it.

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2020>Q 18

A power transmission line feeds input power at $3300 V$ to a step down transformer with its primary windings having $2000$ turns. What should be the number of turns in the secondary in order to get output power at $330 V$ ?

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 7 - Alternating Current>Gujarat Board-2020>Q 19

Derive an expression for current $i$ passing through an AC circuit containing only inductor $L$ . Draw a phasor diagram and graph of $v$ and $i$ versus $ω t$ . Explain instantaneous power and the average power.