6. In a region of uniform magnetic induction B = 10^–2 tesla, a circular coil of radius 30 cm and resistance π² ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is​​

1. 1. 4π2 mA ​

   
   
   

   2. 30 mA ​

   
   
   

   3. 6 mA ​

   
   
   

   4. 200 mA

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​

   I0 =	E0	=	n B A ω
   	R		R

   
   Given, n = 1, B = 10^–2 T, ​
   A = π(0.3)²m², R = π²​ ​
   f = (200/60) and ω = 2π(200/60) ​
   Substituting these values and solving, we get ​
   I₀ = 6 × 10–3 A = 6mA

   Correct Option: C

   ​

   I0 =	E0	=	n B A ω
   	R		R

   
   Given, n = 1, B = 10^–2 T, ​
   A = π(0.3)²m², R = π²​ ​
   f = (200/60) and ω = 2π(200/60) ​
   Substituting these values and solving, we get ​
   I₀ = 6 × 10–3 A = 6mA

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7. An inductor 20 mH, a capacitor 50 µF and a resistor 40Ω are connected in series across a source of emf V = 10 sin 340 t. The power loss in A.C. circuit is :​​

1. 1. 0.51 W

   
   
   

   2. 0.67 W ​

   
   
   

   3. 0.76 W ​

   
   
   

   4. 0.89 W

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​Given: L = 20 mH; C = 50 µF; R = 40 Ω​​V = 10 sin 340 t ​
   ∴​V_runs = 10 / √2
   

   Xc =	1	=	1	= 58.8 Ω
   	ωc		340 x 50 x 10-6

   
   X_L = ωL = 340 × 20 × 10^–3 = 6.8 Ω
   Impedance, Z = √R² + (X_c - X_c)²
   = √40² + (58.8 - 6.8)²
   = √4304 Ω
   Power loss in A.C. circuit,
   

   P = i²rms R =		Vrms	x 89		² R
   		Z

   
   

   =		10/√2				² x 40 =	50 x 40	≈ 0.51 W
   		√4304					4304

   
   

   Correct Option: A

   ​Given: L = 20 mH; C = 50 µF; R = 40 Ω​​V = 10 sin 340 t ​
   ∴​V_runs = 10 / √2
   

   Xc =	1	=	1	= 58.8 Ω
   	ωc		340 x 50 x 10-6

   
   X_L = ωL = 340 × 20 × 10^–3 = 6.8 Ω
   Impedance, Z = √R² + (X_c - X_c)²
   = √40² + (58.8 - 6.8)²
   = √4304 Ω
   Power loss in A.C. circuit,
   

   P = i²rms R =		Vrms	x 89		² R
   		Z

   
   

   =		10/√2				² x 40 =	50 x 40	≈ 0.51 W
   		√4304					4304

   
   

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8. ​Figure shows a circuit that contains three identical resistors with resistance R = 9.0 Ω each, two identical inductors with inductance L = 2.0 mH each, and an ideal battery with emf ε = 18 V. The current 'i' through the battery just after the switch closed is​​
   

1. 1. 0.2 A ​

   
   
   

   2. ​2 A ​

   
   
   

   3. 0 ​

   
   
   

   4. 2 mA

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   At t = 0, no current flows through R₁ and R₃
   
   Current through battery just after the switch closed is
   

   i -	ε	=	18	= 2 A
   	R2		9

   
   

   Correct Option: B

   
   At t = 0, no current flows through R₁ and R₃
   
   Current through battery just after the switch closed is
   

   i -	ε	=	18	= 2 A
   	R2		9

   
   

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9. The current (I) in the inductance is varying with time according to the plot shown in figure. 
   
   Which one of the following is the correct variation of voltage with time in the coil?

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. 
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   V = - L	di
   	dt

   
   

   Here	di	is +ve
   	dt

   
   

   for	T	time and
   	2

   
   

   di	is -ve
   dt

   
   

   for next	T	time so
   	2

   
   

   Correct Option: D

   V = - L	di
   	dt

   
   

   Here	di	is +ve
   	dt

   
   

   for	T	time and
   	2

   
   

   di	is -ve
   dt

   
   

   for next	T	time so
   	2

   
   

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10. ​In an a.c. circuit, the r.m.s. value of current, i_rms is related to the peak current, i₀ by the relation

1. 1. I_rms = √2 I₀

   
   
   

   2. ​I_rms = π I₀

   
   
   

   3. Irms =	1	I0
      	π

   
   
   

   4. Irms =	1	I0
      	√2

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Irms =	I0
   	√2

   
   
   

   Correct Option: D

   Irms =	I0
   	√2

   
   
   

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