Find mutual inductance of (a) (b) (c) (d)

Case1) Magnetic field inside the smaller coil due to large coil is uniform and equal to B = μ i 2 R Thus, flux through the smaller coil due to this magnetic field =. μ i 2 R π r 2 Mutual inductance, M = ϕ i M = μ π r 2 2 R 2 Case 2) Magnetic field inside smaller rectangle due to large rectangle is uniform and equal to μ 0 i a 2 The magnetic flux through this rectangle is ∮ d ϕ = ∮ B . d A ϕ = μ 0 i a 2 . b 2 M = μ 0 a 2 . b 2 M = μ 0 a 2 . b 2 Mutual inductance M = 0 Case (3) Magnetic field inside the smaller coil due to rectangle is B = μ 0 i a b Mutual inductance is given by M = ϕ i M = B A i = μ 0 i a b i π r 2 M = μ 0 π r 2 a b (4) Magnetic field on the axis of a circular coil is B = μ 0 i R 2 2 x 2 + R 2 2 S i n c e , x > > R T h e n B = μ 0 i π R 2 r 2 2 x 3 Magnetic flux linked with the coil is ϕ = B . π r 2 M = ϕ i M = μ 0 i π 2 R 2 r 2 x 3 i

Find time constant for following circuits. (a) (b) (c) (d)

(a) Time constant is given by τ = L R e q In the above circuit resistance are in parallel combination R e q = R 1 R 2 R 1 + R 2 τ = L R 1 + R 2 R 1 R 2 (b) In this circuit i R e q = R 1 R 2 R 3 R 1 + R 2 + R 3 Now, time constant τ = L R 1 R 2 R 3 R 1 + R 2 + R 3 (c) In this circuit equivalent resistance is R p = 1 R + 1 2 R = 2 R 3 R e q = 2 R 3 + 2 R 3 R e q = 4 R 3 Time constant τ = 3 L 4 R (d) IN this circuit equivalent resistance is R p = 1 3 R + 1 6 R = 2 R R e q = 2 R + 2 R R e q = 4 R Time constant is τ = L 4 R

Find current ( i ) at time t = 0 and time t = ∞ in the following circuits. (a) (b) (c) (d)

(a) For circuit a At t = 0 and t = ∞ the circuit will act as a short circuit so current will be i = E R (b) For circuit a At t = 0 Apply kirchoff's voltage law E - i - E R R - i - E R = 0 ⇒ E - i R + E - i R + E = 0 ⇒ i = 3 E 2 R (c) For circuit c At t = 0 L will be short circuited i = E 3 . 5 R (d) For circuit d At t = 0 and t = ∞ L is short circuited i = E R

E M B I B E

Gamma Question Bank for Engineering Physics>Class XII>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5

Embibe Experts Solutions for Exercise 5: EXERCISE 6.5

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Embibe Experts Physics Solutions for Exercise - Embibe Experts Solutions for Exercise 5: EXERCISE 6.5

Attempt the practice questions from Exercise 5: EXERCISE 6.5 with hints and solutions to strengthen your understanding. Gamma Question Bank for Engineering Physics solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Exercise 5: EXERCISE 6.5 with Hints & Solutions

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 33

Current in the primary coil of a mutual inductor is $2 A$ and is increasing at the rate of $3 A s^{- 1}$ . If the mutual inductance is $4 H$ , find flux and emf in the secondary coil.

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 34

Find mutual inductance of

(a) Question Image (b)

(c) Question Image (d)

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 35

An inductor $(L = 100 mH),$ a resistor $(R = 100 Ω)$ and a battery $(E = 100 V)$ are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short-circuiting points $A$ and $B$ . The current in the circuit, $1 ms$ after the short circuit is:

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 36

Find time constant for following circuits.

(a) Question Image (b)

(c) Question Image (d)

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 37

Switch was in position $1$ for a long time. It is suddenly switch to position $2$ . Find voltage drop across inductor immediately after the switch is toggled.

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 38

Key is closed at time $t = 0$ . $i = i_{1}$ at $t = 0$ and $i = i_{2}$ at time $t = \infty$ . $\frac{i_{1}}{i_{2}}$ equals

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Gamma Question Bank for Engineering Physics>Chapter 20 - Electromagnetic Induction>EXERCISE 6.5>Q 39

Switch is in position $A$ for a long time. It is suddenly switched to the side $B$ . Mass of rod is $m$ and length is I. Maximum speed of rod will be .....

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