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A 4000 V/2000 V, 60 Hz single phase transformer has a total impedance of 60 Ω referred to the primary side. The primary and secondary windings have negligible resistances. If the transformer supplies a resistive of 20 Ω, the full load voltage at the secondary side will be
- a)1143 V
- b)1600 V
- c)2000 V
- d)3200 V
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A 4000 V/2000 V, 60 Hz single phase transformer has a total impedance ...
Ohms. The primary winding has 200 turns. Calculate the secondary winding turns, the primary current, and the secondary current.
Given data:
Primary voltage (V1) = 4000 V
Secondary voltage (V2) = 2000 V
Frequency (f) = 60 Hz
Total impedance (Z) = 60 ohms
Number of turns in primary winding (N1) = 200
1. Calculate the secondary winding turns (N2):
Voltage ratio = V1/V2 = N1/N2
N2 = N1 * (V2/V1)
N2 = 200 * (2000/4000)
N2 = 100
Therefore, the secondary winding has 100 turns.
2. Calculate the primary current (I1):
Impedance (Z) = V1/I1
I1 = V1/Z
I1 = 4000/60
I1 = 66.67 A
Therefore, the primary current is 66.67 A.
3. Calculate the secondary current (I2):
Current ratio = I1/I2 = N2/N1
I2 = I1 * (N1/N2)
I2 = 66.67 * (200/100)
I2 = 133.33 A
Therefore, the secondary current is 133.33 A.
Given data:
Primary voltage (V1) = 4000 V
Secondary voltage (V2) = 2000 V
Frequency (f) = 60 Hz
Total impedance (Z) = 60 ohms
Number of turns in primary winding (N1) = 200
1. Calculate the secondary winding turns (N2):
Voltage ratio = V1/V2 = N1/N2
N2 = N1 * (V2/V1)
N2 = 200 * (2000/4000)
N2 = 100
Therefore, the secondary winding has 100 turns.
2. Calculate the primary current (I1):
Impedance (Z) = V1/I1
I1 = V1/Z
I1 = 4000/60
I1 = 66.67 A
Therefore, the primary current is 66.67 A.
3. Calculate the secondary current (I2):
Current ratio = I1/I2 = N2/N1
I2 = I1 * (N1/N2)
I2 = 66.67 * (200/100)
I2 = 133.33 A
Therefore, the secondary current is 133.33 A.
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Community Answer
A 4000 V/2000 V, 60 Hz single phase transformer has a total impedance ...
Concept:
Consider a two winding single phase transformer as shown below,
N1 = primary winding turns
N2 = secondary winding turns
V1 = primary winding voltage
V2 = secondary winding voltage
I1 = current through the primary winding
I2 = current through the secondary winding
Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by k.
K=N2N1=V2V1=I1I2" tabindex="0">K=N2N1=V2V1=I1I----- (1)Transformer equivalent circuit with respect to secondary can be represented a show below
Where R02 = Effective resistance referred to the secondary side of the transformer.
R02 = R2 + R1' ........ (2)
R1' = Primary winding resistance as referred to the secondary side.
R1' = R1 × k2 ......... (3)
Similarly, the effective resistance referred to the primary side of the transformer is given as,
R01 = R1 + R2'
R2' = Secondary winding resistance as referred to the primary side.
R2' = R2 / k2
Calculation:
Given total impedance of the transformer referred to primary R01 = 60 Ω
Transformation ratio k = V2 / V1 = 2000 / 4000 = 0.5
Total impedance of the transformer referred to secondary when primary and secondary windings have negligible resistances is given as
R02 = R01 × k2
= 60 / 4 = 15 Ω
Apply the voltage division rule to find voltage across the load
VL = 2000 × 20 / (15 + 20)
VL = 1143 V
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