26. An inductance L having a resistance R is connected to an alternating source of angular frequency ω. The quality factor Q of the inductance is​​

1. 1. 	R
      	ωL

   
   
   

   2. 		ωL			²
      		R

   
   
   

   3. 		R			1/2
      		ωL

   
   
   

   4. 	ωL
      	R

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Quality Factor =	Potential drop accross capacitor or inductor
   	Potential drop accross R

   
   

   =	IωL	=	ωL
   	IR		R

   
   

   Correct Option: D

   Quality Factor =	Potential drop accross capacitor or inductor
   	Potential drop accross R

   
   

   =	IωL	=	ωL
   	IR		R

   
   

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27. A capacitor has capacity C and reactance X. If capacitance
    and frequency become double, then reactance will be​​

1. 1. 4X ​

   
   
   

   2. X/2 ​

   
   
   

   3. X/4 ​

   
   
   

   4. ​2X

   
   
   

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1. View Hint View Answer Discuss in Forum

   Capacitive reactance,
   

   X =	1	=	1
   	ωC		2πƒC

   
   

   ⇒ X ∝	1
   	ƒ C

   
   

   ∴

   X'

   =

   ƒ

   ×

   C

   ƒ

   ×

   C

   =

   1

   X

   ƒ'

   C'

   2ƒ

   2C

   4

   
   

   ⇒ X' =	X
   	4

   
   

   Correct Option: C

   Capacitive reactance,
   

   X =	1	=	1
   	ωC		2πƒC

   
   

   ⇒ X ∝	1
   	ƒ C

   
   

   ∴

   X'

   =

   ƒ

   ×

   C

   ƒ

   ×

   C

   =

   1

   X

   ƒ'

   C'

   2ƒ

   2C

   4

   
   

   ⇒ X' =	X
   	4

   
   

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28. In a series resonant circuit, having L, C and R as its elements, the resonant current is i. The power dissipated in the circuit at resonance is
    where ω is the angular resonance frequency.

1. 1. 	i²R
      	[ωL -(1/ωC)]

   
   
   

   2. zero

   
   
   

   3. i²ωL

   
   
   

   4. π²R

   
   
   

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1. View Hint View Answer Discuss in Forum

   At resonance Lω =	1	,ω
   	Cω

   
   

   =	1
   	√LC

   
   

   Current through circuit i =	E
   	R

   
   Power dissipated at Resonance = i²R

   Correct Option: D

   At resonance Lω =	1	,ω
   	Cω

   
   

   =	1
   	√LC

   
   

   Current through circuit i =	E
   	R

   
   Power dissipated at Resonance = i²R

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29. A coil of 40 henry inductance is connected in series with a resistance of 8 ohm and the combination is joined to the terminals of a 2 volt battery. The time constant of the circuit is
    

1. 1. 20 seconds

   
   
   

   2. ​5 seconds ​

   
   
   

   3. 1/5 seconds ​

   
   
   

   4. ​40 seconds

   
   
   

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1. View Hint View Answer Discuss in Forum

   Time constant is L/R ​
   Given, L = 40H & R = 8Ω ​
   ∴ τ = 40/8 = 5 sec.

   Correct Option: B

   Time constant is L/R ​
   Given, L = 40H & R = 8Ω ​
   ∴ τ = 40/8 = 5 sec.

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30. In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is​​

1. 1. 	1
      	πƒ(2πƒL - R)

   
   
   

   2. 	1
      	2 πƒ(2πƒL - R)

   
   
   

   3. 	1
      	πƒ(πƒL + R)

   
   
   

   4. 	1
      	πƒ(2πƒL + R)

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​From figure,
   
   

   tan 45º =	(1/ωC) - ωL
   	R

   
   

   ⇒	1	- ωL = R
   	ωC

   
   

   ⇒	1	= R + ωL
   	ωC

   
   

   		∴ ω =	2π	= 2μƒ
   			T

   
   

   C =	1	=	1
   	ω(R + ωL)		2πƒ(R + 2πƒ L)

   
   

   Correct Option: D

   ​From figure,
   
   

   tan 45º =	(1/ωC) - ωL
   	R

   
   

   ⇒	1	- ωL = R
   	ωC

   
   

   ⇒	1	= R + ωL
   	ωC

   
   

   		∴ ω =	2π	= 2μƒ
   			T

   
   

   C =	1	=	1
   	ω(R + ωL)		2πƒ(R + 2πƒ L)

   
   

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