(a)
The current that would have to flow through the copper wires.
(a)
Answer to Problem 97P
The current that would have to flow through the copper wires is
Explanation of Solution
Write the equation for the average power.
Here,
Rewrite the above equation for
Conclusion:
Given that the average power is
Substitute
Therefore, the current that would have to flow through the copper wires is
(b)
The power dissipated due to the resistance of the copper wires.
(b)
Answer to Problem 97P
All of the power is converted into internal energy in the copper wires.
Explanation of Solution
Write the equation for the power converted in the wires due to the resistance.
Here,
Conclusion:
Given that the resistance of the copper wires is
Substitute
But the average power at which the voltage is sent is
Thus, all of the power is converted into internal energy in the copper wires since
(c)
The current flowing through the wires when the transformers are used.
(c)
Answer to Problem 97P
The current flowing through the wires when the transformers are used is
Explanation of Solution
Equation (II) can be used to determine the value of the current.
Conclusion:
Given that the rms value of the voltage sent is
Substitute
Therefore, the current flowing through the wires when the transformers are used is
(d)
The power dissipated due to the resistance of the wires when the transformers are used and the percent of this value with respect to the total power output of the power plant.
(d)
Answer to Problem 97P
The power dissipated due to the resistance of the wires when the transformers are used is
Explanation of Solution
Equation (III) can be used to determine the power dissipated.
Conclusion:
Substitute
Find the percent of this power loss is of the total power output of the power plant.
Therefore, the power dissipated due to the resistance of the wires when the transformers are used is
(e)
The number of secondary turns the transformer should have.
(e)
Answer to Problem 97P
The number of secondary turns the transformer should have is
Explanation of Solution
Write the equation for a transformer.
Here,
Rewrite the above equation for
Conclusion:
Given that the number of turns in the primary coil is
Substitute
Therefore, the number of secondary turns the transformer should have is
Therefore, the average power dissipated in the wires when using the transformer is
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