71. The voltage of generator and an infinite bus are given as 0.92 ∠10° and 1.0∠0° respectively. The generator acts as a

1. 1. shunt coil

   
   
   

   2. shunt capacitor

   
   
   

   3. the data is insufficient to judge

   
   
   

   4. none of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: A

   NA

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72. It x is the system reactance and r is its resistance, the power transferred is maximum when

1. 1. x = r

   
   
   

   2. x = √2r

   
   
   

   3. x = √3r

   
   
   

   4. x = 2r

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   

   I =	V1∠δ - V2∠0
   	Z∠θ

   
   

   =	V1	∠(δ - ∠0) -	V2	∠- θ
   	Z		Z

   
   Power received, P₂ = Re [V₂I*]
   

   = Re		V2		V1	∠(θ - δ) -	V2	∠θ
   				Z		Z

   
   

   =	V1V2	cos(θ - δ) -	V²2	cos θ
   	Z		Z

   
   Let θ = 90° – α, then
   

   =	V1V2	cos(90° - α - δ) -	V²2	cos(90° - α)
   	Z		Z

   
   

   =	V1V2	sin(α + δ) -	V²2	sin α
   	Z		Z

   
   

   P2 max =	V1V2	-	V²2	sin α[α + δ = 90°]
   	Z		Z

   
   

   As, sin α =	r	, then
   	Z

   
   

   P2 max =	V1V2	-	V²2	.	r
   	√r² + x²		√r² + x²		√r² + x²

   
   For P_{2 max} to be maximum,
   

   dP2 max	= 0
   dx

   
   

   or V²2		x1	-	2xr		= 0
   		(r² + x²)2/3		(r² + x²)²

   
   Here V₁ = V₂
   ∴ r² + x² = 4r²
   or x = √3r

   Correct Option: C

   
   

   I =	V1∠δ - V2∠0
   	Z∠θ

   
   

   =	V1	∠(δ - ∠0) -	V2	∠- θ
   	Z		Z

   
   Power received, P₂ = Re [V₂I*]
   

   = Re		V2		V1	∠(θ - δ) -	V2	∠θ
   				Z		Z

   
   

   =	V1V2	cos(θ - δ) -	V²2	cos θ
   	Z		Z

   
   Let θ = 90° – α, then
   

   =	V1V2	cos(90° - α - δ) -	V²2	cos(90° - α)
   	Z		Z

   
   

   =	V1V2	sin(α + δ) -	V²2	sin α
   	Z		Z

   
   

   P2 max =	V1V2	-	V²2	sin α[α + δ = 90°]
   	Z		Z

   
   

   As, sin α =	r	, then
   	Z

   
   

   P2 max =	V1V2	-	V²2	.	r
   	√r² + x²		√r² + x²		√r² + x²

   
   For P_{2 max} to be maximum,
   

   dP2 max	= 0
   dx

   
   

   or V²2		x1	-	2xr		= 0
   		(r² + x²)2/3		(r² + x²)²

   
   Here V₁ = V₂
   ∴ r² + x² = 4r²
   or x = √3r

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73. A motor is receiving 25% of the power that it is capable of receiving from an infinite bus. If load of the motor is doubled, then maximum value of δ during swinging of the rotor ar ound it s new equilibrium position will be

1. 1. 40°

   
   
   

   2. > 30°

   
   
   

   3. < 30°

   
   
   

   4. 25°

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   sin δ₀ = 0.25,
   ⇒ δ₀ = 14.48°
   sin δ_c = 0.5,
   ⇒ δ₀ = 30°
   
   or 0.5 (δ_m – 0.2527) = (cos δ₀ – cos δ_m)
   or 0.5 δ_m = cos δ₀ – cos δ_m + 0.1263
   For solution of this we make guess for δ_m such that δ_m should be greater than 30° (as δ_c = 30°).
   After some trials, δ_m is found to be 45°.

   Correct Option: B

   
   sin δ₀ = 0.25,
   ⇒ δ₀ = 14.48°
   sin δ_c = 0.5,
   ⇒ δ₀ = 30°
   
   or 0.5 (δ_m – 0.2527) = (cos δ₀ – cos δ_m)
   or 0.5 δ_m = cos δ₀ – cos δ_m + 0.1263
   For solution of this we make guess for δ_m such that δ_m should be greater than 30° (as δ_c = 30°).
   After some trials, δ_m is found to be 45°.

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74. An ideal voltage source is connected across a variable resistance. The variation of current as a function of resistance is given by

1. 1. a straight line passing through the origin

   
   
   

   2. a ractangular hyperbola

   
   
   

   3. a parabola

   
   
   

   4. all of the above

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: B

   NA

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75. In a synchronous machine, in case the axis of field flux is in line with the armature flux, the machine is working

1. 1. as synchronous moter

   
   
   

   2. as synchronous generator

   
   
   

   3. as floating machine

   
   
   

   4. the machine will not work

   
   
   

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1. View Hint View Answer Discuss in Forum

   NA

   Correct Option: C

   NA

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