21. ​Two coils of self inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is

1. 1. 6 mH

   
   
   

   2. 4 mH

   
   
   

   3. 16 mH

   
   
   

   4. 10 mH

   
   
   

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1. View Hint View Answer Discuss in Forum

   Mutual Inductance of two coils
   M = √M₁M₂ = √2mH × 8mH = 4mH

   Correct Option: B

   Mutual Inductance of two coils
   M = √M₁M₂ = √2mH × 8mH = 4mH

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22. In an inductor of self-inductance L = 2 mH, current changes with time according to relation i = t²e^–t. At what time emf is zero?

1. 1. 4s

   
   
   

   2. 3s

   
   
   

   3. 2s

   
   
   

   4. 1s

   
   
   

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1. View Hint View Answer Discuss in Forum

   L = 2mH, i = t²e^–t
   

   E = - L	di	= - L[-t2e–t + 2te-t]
   	dt

   
   when E = 0,
   - e^-te^–t + 2te^-t = 0
   or,  2t e^-t = e^-t t²
   ⇒   t = 2 sec.

   Correct Option: C

   L = 2mH, i = t²e^–t
   

   E = - L	di	= - L[-t2e–t + 2te-t]
   	dt

   
   when E = 0,
   - e^-te^–t + 2te^-t = 0
   or,  2t e^-t = e^-t t²
   ⇒   t = 2 sec.

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23. Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to equation I = I₀ sin ωt, where I₀ = 10A and ω = 100π radian/sec. The maximum value of e.m.f. in the second coil is

1. 1. 2π

   
   
   

   2. 5π

   
   
   

   3. π

   
   
   

   4. 4π

   
   
   

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1. View Hint View Answer Discuss in Forum

   e = - M	di
   	dt

   
   

   = - 0.005 ×	d(i0 sinωt)
   	dt

   
   = –0.005 × i₀ ×(ω cos ωt)
   e_max = –0.005 × i₀ × ω (when cos ω t = -1)
   = 0.005 × 10 × 100π = 5π V

   Correct Option: B

   e = - M	di
   	dt

   
   

   = - 0.005 ×	d(i0 sinωt)
   	dt

   
   = –0.005 × i₀ ×(ω cos ωt)
   e_max = –0.005 × i₀ × ω (when cos ω t = -1)
   = 0.005 × 10 × 100π = 5π V

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24. A conductor of length 0.4 m is moving with a speed of 7 m/s perpendicular to a magnetic field of intensity 0.9 Wb/m². The induced e.m.f. across the conductor is

1. 1. 1.26 V

   
   
   

   2. 2.52 V ​

   
   
   

   3. 5.04 V

   
   
   

   4. 25.2 V

   
   
   

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1. View Hint View Answer Discuss in Forum

   Length of conductor (l) = 0.4 m; Speed (v) = 7 m/s and magnetic field (B) = 0.9 Wb/ m². Induced e.m.f. (V) = Blv sin θ = 0.9 × 0.4 × 7 × sin 90º = 2.52 V.

   Correct Option: B

   Length of conductor (l) = 0.4 m; Speed (v) = 7 m/s and magnetic field (B) = 0.9 Wb/ m². Induced e.m.f. (V) = Blv sin θ = 0.9 × 0.4 × 7 × sin 90º = 2.52 V.

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25. A varying current in a coil changes from 10A to zero in 0.5 sec. If the average e.m.f induced in the coil is 220V, the self-inductance of the coil is

1. 1. 5 H

   
   
   

   2. 6 H

   
   
   

   3. 11 H

   
   
   

   4. 12 H

   
   
   

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1. View Hint View Answer Discuss in Forum

   Initial current (I₁) = 10 A; Final current(I₂)= 0; Time (t) = 0.5 sec and induced e.m.f. (ε) = 220 V. ​Induced e.m.f. (ε)
   

   = - L	dI	= - L	(I2 - I1)
   	dt		t

   
   

   = - L	(0 - 10)	= 20L
   	0.5

   
   

   or, L =	220	= 11 H
   	20

   
   [where L = Self inductance of coil]

   Correct Option: C

   Initial current (I₁) = 10 A; Final current(I₂)= 0; Time (t) = 0.5 sec and induced e.m.f. (ε) = 220 V. ​Induced e.m.f. (ε)
   

   = - L	dI	= - L	(I2 - I1)
   	dt		t

   
   

   = - L	(0 - 10)	= 20L
   	0.5

   
   

   or, L =	220	= 11 H
   	20

   
   [where L = Self inductance of coil]

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