Power loss in the transmission system with a transformer

In summary: You correctly calculated the power lost in the cables and the efficiency of the transmission system. You also understood how a transformer works in step-down mode to increase the voltage and decrease the current. Your final calculation for the power loss in the new transmission system is correct as well. In summary, you correctly calculated the power loss in the cables, the voltage developed by the generator, the efficiency of the transmission system, and the power loss in the new transmission system using a transformer. You also demonstrated a good understanding of how a transformer works in step-down mode. Great work!
  • #1
moenste
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Homework Statement


A farmer installs a private hydroelectric generator to provide power for equipment rated at 120 kW 240 V AC. The generator is connected to the equipment by two conductors which have a total resistance of 0.20 Ω. The system is shown schematically in Fig. 1.

b83acd9e4768.jpg


(a) The equipment is operating at its rated power. Calculate: (i) the power loss in the cables, (ii) the voltage which must be developed by the generator, (iii) the efficiency of the transmission system.

(b) An engineer suggests that the farmer uses a transformer to convert the generator output to give a PD of 2400 V at the end of the transmission line, as shown in Fig. 2. A second transformer is to be used to step down this PD to 240 V.

e9a7984d235d.jpg


(i) Explain briefly how a transformer makes use of electromagnetic induction to produce an output voltage several times bigger than the input voltage.
(ii) The transformers are 100 % efficient. Calculate the power loss in the new transmission system.

Answers: (a) (i) 50 kW, (ii) 340 V, (iii) 70.6 %, (b) (ii) 500 W.

2. The attempt at a solution
(a) (i) P = V I → I = P / V = 120 000 / 240 = 500 A. P = I2 R = 5002 * 0.2 = 50 kW.

(a) (ii) V = P / I = 50 000 / 500 = 100 V in the cables plus 240 V in the equipment so 340 V in total.

(a) (iii) Efficiency = 120 000 / (120 000 + 50 000) = 0.706 or 70.6 %.

(b) (ii) This one I'm not sure. I found the power: P = V2 / R = 24002 / 0.2 = 28 800 000 W and current I = V / R = 2400 / 0.2 = 12 000 A. And also current in the equpment: I = P / V = 120 000 / 240 = 500 A. But I'm not sure whether I'm going in the right direction. The numbers are so largely different.
 
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  • #2
moenste said:
(b) (ii) This one I'm not sure. I found the power: P = V2 / R = 24002 / 0.2 = 28 800 000 W and current I = V / R = 2400 / 0.2 = 12 000 A. And also current in the equpment: I = P / V = 120 000 / 240 = 500 A. But I'm not sure whether I'm going in the right direction. The numbers are so largely different.

The 2400 V is NOT developed across the cable resistance! The 2400 V is developed across the primary of the step-down load transformer. So your power calculation for the cable loss is not correct.

What you want to do is determine the current in the cables and use that to find the power lost in the cable resistance.
 
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  • #3
moenste said:
And also current in the equpment: I = P / V = 120 000 / 240 = 500 A.
Right.
moenste said:
. I found the power: P = V2 / R = 24002 / 0.2 = 28 800 000 W and current I = V / R = 2400 / 0.2 = 12 000 A.
No. Have you studied how a transformer works? Power input to the primary=power output at the secondary(+transformer losses(which are zero here)) is the principle here. What is the input power to the primary?
 
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  • #4
gneill said:
The 2400 V is NOT developed across the cable resistance! The 2400 V is developed across the primary of the step-down load transformer. So your power calculation for the cable loss is not correct.

What you want to do is determine the current in the cables and use that to find the power lost in the cable resistance.
cnh1995 said:
Right.

No. Have you studied how a transformer works? Power input to the primary=power output at the secondary(+transformer losses(which are zero here)) is the principle here. What is the input power to the primary?
I E = I E
2400 I = 240 * 500
I = 50 A.

P = I2 R = 502 * 0.2 = 500 W.

Should be correct.
 
  • #5
moenste said:
I E = I E
2400 I = 240 * 500
I = 50 A.

P = I2 R = 502 * 0.2 = 500 W.

Should be correct.
Good job!
 
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Related to Power loss in the transmission system with a transformer

1. What causes power loss in the transmission system with a transformer?

Power loss in the transmission system with a transformer is mainly caused by the resistance of the transformer's windings and the core losses due to hysteresis and eddy currents.

2. How does the design of a transformer affect power loss in the transmission system?

The design of a transformer, such as the number of turns in the windings and the type of core material used, can greatly affect power loss in the transmission system. A well-designed transformer can reduce power loss and increase efficiency.

3. Can power loss be eliminated completely in a transformer?

No, it is not possible to completely eliminate power loss in a transformer. However, it can be reduced through careful design and regular maintenance.

4. How does the length of the transmission line affect power loss in a transformer?

The longer the transmission line, the higher the power loss in a transformer. This is due to the resistance of the wires and the voltage drop that occurs over longer distances.

5. What are some ways to reduce power loss in a transmission system with a transformer?

Some ways to reduce power loss in a transmission system with a transformer include using thicker wires with lower resistance, using high-quality core materials, and regularly maintaining and repairing any faults in the system.

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