Ques.61. A balanced three-phase star-connected load draws power from a 440V supply. The two connected wattmeters, W1 and W2, indicates 5 kW and 1200 W respectively. Calculate the current in the circuit.
11.52 A✓
15.56 A
1.11 A
10.11 A
As given in the above question
W1 = 5 kW
W2 = 1200 W
VL = 440 V
The power factor of the two wattmeters is
tanØ = √3[(W1 – W2) / (W1 + W2)]
tanØ = √3[(5000 – 1200) ⁄ (5000 + 1200)]
Φ = 45°
Power factor = cosφ = cos45° = 0.707
Total power
W = W1 + W2 = 5000 + 1200 = 6200W
Active power in star connected system
W = √3.VL.IL.cosφ
6200 = √3 × 440 × IL × 0.707
IL = 11.52 A
Ques.62. The two-wattmeter method is used to measure the input power of a three-phase induction motor. If the two wattmeter readings are 1,700 W and 1,100 W. determine the input current drawn from a 440 V, 3-phase AC supply.
0.54 A
0.32 A
4 A✓
0.525 A
As given in the above question
W1 = 1700 W
W2 = 1100 W
VL = 440 V
The power factor of the two wattmeters is
tanØ = √3[(W1 – W2) / (W1 + W2)]
tanØ = √3[(1700 – 1100) ⁄ (1700 + 1100)]
Φ = 20.30°
Power factor = cosφ = cos20.30° = 0.93
Total power
W = W1 + W2 = 1700 + 1100 = 2800W
Input power
P = √3.VL.IL.cosφ
2800 = √3 × 440 × IL × 0.93
IL = 4 A
Ques.63. A three-phase, balanced, delta-connected load of (4 + j8)Ω is connected to a 400-V, 3-φ balanced power supply. Assuming that the phase sequence is RYB, determine the phase current IR.
45.74∠−63.4°A
44.74∠−63.4°A✓
45.74∠63.4°A
44.74∠63.4°A
Given
Voltage = 400 V
Zph = (4 + j8)
|Zph| = (42 + 82)1/2
|Zph| = 8.94 Ω
θ = tan−1(b/a) = tan−1(8/4) = 63.4⁰
= tan−1(8/4)
Impedance per phase = (4+j8) Ω = 8.94∠63.4⁰Ω
Taking the line voltage VRY = V∠0⁰ as a reference VRY = 400∠0⁰V, VYB = 400∠-120⁰V and VBR = 400∠-240⁰V.
In delta connected system line voltage is equal to the phase voltage
VP = VL = 400 V
IP = Vp/Zp
IP = 400∠0o)/(8.94∠63.4o )
IP = 44.74∠−63.4⁰A.
Ques.64. A standard sinusoidal current wave changes its polarity at___
Negative Value
Zero Value✓
Minimum Value
Maximum Value
Many a time, alternating voltages and currents are represented by a sinusoidal wave, or simply a sinusoid. The sinusoidal wave is generally referred to as a sine wave. Basically, an alternating voltage (current) waveform is defined as the voltage (current) that fluctuates with time periodically, with the change in polarity and direction.
Changing polarity refers to changing from positive to negative or negative to positive. For currents, it refers to the current flowing in one direction and then flowing in the opposite direction.
The period can be measured in the following different ways
1. From zero crossing of one cycle to zero crossing of the next cycle.
2. From positive peak of one cycle to the positive peak of the next cycle.
3. From the negative peak of one cycle to negative peak oil the next cycle.
Ques.65. If Q is the charge and C be the capacitance, then the energy stored in the capacitor is given by_____
Q/2C
QC/2
Q2/2C✓
1/QC
The capacitance of a capacitor is defined as the measure of the charge stored by the capacitor per unit voltage; C = Q/V
Hence Q = CV
Energy stored In the charged capacitor
When a capacitor is charged by a voltage source (say battery) it stores the electric energy. If C = capacitance of the capacitor; Q = charge on capacitor and V is the potential difference across capacitor then energy stored in the capacitor is given by
U = CV2/2 = Q2/2 = QV/2
Ques.66. The two-wattmeter method is used to measure a three-phase power supply. If the two wattmeter readings are 2 kW and 500 W. Determine the total power of the circuit.
25 kW
250 W
2.5 kW✓
25 W
W1 = 2 kW = 2000 kW
W2 = 500 W
Total active power = W1 + W2 = 2000 + 500 = 2.5 kW
Ques.67. According to Gauss’s law, if E is _______, the charge density in the ideal conductor is zero.
Positive
Negative
Zero✓
Unity
A conductor contains moving free charges. An isolated conductor is shown in Figure. Let an external electric field E be applied to it. A force will get applied on the charges inside the conductor. As a result, charges will get accumulated on the surface. These induced charges generate a counteracting internally induced field Ei. This internally induced field Eiopposes and cancels the externally applied field E.
Thus, there does not exist any electrostatic field inside a perfect conductor. As a result E = -∇ V = 0.
It implies that the potential is the same at every point inside the conductor. According to Gauss’s Law, the charge density inside a perfect conductor is zero if E= 0.
Therefore,
ρv = 0
The perfect conductor is characterized by the following properties:
The electric field inside and on the surface of the perfect conductor is zero E = 0.
The total charge of the conductor is distributed on its surface so that the electric field in the conductor and on its surface remains always zero.
The electrical field is always normal to the surface of the perfect conductor, and there is no electric field component tangential to its surface. Accordingly, the electric flux density D is normal to the surface and equal to the total charge on the surface of the conductor.
The electric potential inside and on the surface of the conductor is constant since E = –∇ V = 0. Thus, the surface of the conductor is equipotential.
Ques.68. What is the relationship between the line voltage and the phase voltage in a delta -connected load?
Line voltage = Phase current
Line voltage > Phase voltage
Line voltage < Phase voltage
Line voltage = Phase voltage✓
In delta connected system the line voltage is equal to the phase voltage and the Line current is √3 times of Phase Current.
Ques.69. A 10μF capacitor in series with a 1-MΩ resistor is connected across a 100-V DC supply. The initial rate of rise of voltage across the capacitor is
0.1V/s
10V/s✓
1V/s
0.01V/s
Given
Capacitor,C = 10μF = 10 × 10−6
Resistance R = 1-MΩ = 1 × 106
Voltage V = 100 V
The initial rate of rise of voltage across the capacitor is given as
= 100 ⁄ (10 × 10−6) × (1 × 106)
= 10 V/s
Ques.70. Find the phase voltage if a three-phase star-connected system is connected to a 400V 50 Hz AC supply. Assume Zph consists of a resistance of 10Ω in series With an inductance of 0.0318 H.
400 V
230.94 V✓
230 V
110.24 V
In three phase star connected system the phase voltage is given as
