1. In an ac circuit an alternating voltage e = 200√2 sin 100 t volts is connected to a capacitor of capacity 1 µF. The r.m.s. value of the current in the circuit is​​

1. 1. ​10 mA ​

   
   
   

   2. 100 mA ​

   
   
   

   3. 200 mA ​

   
   
   

   4. 20 mA

   
   
   

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1. View Hint View Answer Discuss in Forum

   Vrms =	200√2	= 200V
   	√2

   
   

   Irms =	Vrms	=	200/1	= 2 x 10-2 = 20 mA
   	Xc		100 x 10-6

   
   
   

   Correct Option: D

   Vrms =	200√2	= 200V
   	√2

   
   

   Irms =	Vrms	=	200/1	= 2 x 10-2 = 20 mA
   	Xc		100 x 10-6

   
   
   

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2. In an a.c circuit the e.m.f. (e) and the current (i) at any instant are given respectively by ​
   e = E₀ sin ωt ​
   i = I₀ sin (ωt – φ) ​
   The average power in the circuit over one cycle of a.c. is ​​

1. 1. 	E0I0
      	2

   
   
   

   2. 	E0I0	sin φ
      	2

   
   
   

   3. 	E0I0	cos φ
      	2

   
   
   

   4. E₀I₀

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​The average power in the circuit over one cycle of a.c. is given by ​
   P^av = e^rms × i^rms × cosφ
   

   =	E0	.	I0	. cos f =	E0 I0	cos f
   	√2		√2		2

   
   

   Correct Option: C

   ​The average power in the circuit over one cycle of a.c. is given by ​
   P^av = e^rms × i^rms × cosφ
   

   =	E0	.	I0	. cos f =	E0 I0	cos f
   	√2		√2		2

   
   

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3. The r.m.s. value of potential difference V shown in the figure is​​
   

1. 1. V₀​

   
   
   

   2. V₀/√2

   
   
   

   3. V₀/2 ​

   
   
   

   4. V₀/√3
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   Correct Option: B

   
   

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4. In an A.C. circuit with voltage V and current I the power dissipated is​​

1. 1. dependent on the phase between V and I ​

   
   
   

   2. 	1	VI
      	√2

   
   
   

   3. 	1	VI
      	2

   
   
   

   4. VI

   
   
   

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1. View Hint View Answer Discuss in Forum

   Power dissipated = E^rms. I^rms = (E^rms) (I^rms) cos θ
   Hence, power dissipated depends upon phase difference.
   

   Correct Option: A

   Power dissipated = E^rms. I^rms = (E^rms) (I^rms) cos θ
   Hence, power dissipated depends upon phase difference.
   

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5. ​The instantaneous values of alternating current and voltages in a circuit are given as
   

   i =	1	sin(100πt) amper
   	√2

   
   

   e =	1	sin(100πt/3) volt
   	√2

   
   The average power in Watts consumed in the circuit is :​​
   

1. 1. 	1
      	4

   
   
   

   2. 	√3
      	4

      
      

   
   
   

   3. 	1
      	2

   
   
   

   4. 	1
      	8

      
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   ​The average power in the circuit  where cos φ = power factory ​
   < P > = V_rms × I_rms cos φ
   

   φ = π/3 = phase difference =	180	= 60
   	3

   
   

   Vrms =	1/√2	=	1	Volt
   	√2		2

   
   

   Irms =	1/√2	=	1	Volt
   	√2		2

   
   

   cos φ =	π	=	1
   	3		2

   
   

   < p > =	1	x	1	x	1	=	1	W
   	2		2		2		8

   
   

   Correct Option: D

   ​The average power in the circuit  where cos φ = power factory ​
   < P > = V_rms × I_rms cos φ
   

   φ = π/3 = phase difference =	180	= 60
   	3

   
   

   Vrms =	1/√2	=	1	Volt
   	√2		2

   
   

   Irms =	1/√2	=	1	Volt
   	√2		2

   
   

   cos φ =	π	=	1
   	3		2

   
   

   < p > =	1	x	1	x	1	=	1	W
   	2		2		2		8

   
   

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