The step-down transformer in a local neighborhood reduces the voltage from a 7,200 V line to 120 V. (a) If there are 125 loops on the secondary, how many are on the primary coil? (b) What current does the transformer draw from the line if the current in the secondary is 36 A? (c) What are the power input and output?
(a)
The number of loops at the primary side of a step-down transformer.
Answer to Problem 15PEB
Solution:
The number of loops at the primary side is
Explanation of Solution
Given data:
A step-down transformer with 125 loops on the secondary side. The voltage at the primary side is
Formula used:
The expression that relates the number of loops and the voltage is written as,
Here,
Also, power and current can be determined by the formula, therefore
Here,
Explanation:
Consider the expression,
Rearrange to get the secondary voltage
Substitute
Conclusion:
Hence, the number of loops ate the primary side is
(b)
The primary current in a step down transformer.
Answer to Problem 15PEB
Solution:
The primary current is
Explanation of Solution
Given data:
A step-down transformer with 125 loops on the secondary side. The voltage at the primary side is
Formula used:
The expression for power in a transformer is written as,
Here,
Explanation:
Consider the expression for power in the transformer.
Rearrange the power expression to get the primary current
Substitute
Conclusion:
Hence, the primary current is
(c)
The power of the transformer at the input and the output sides.
Answer to Problem 15PEB
Solution: The power at the input and the output side is same and is equal to
Explanation of Solution
Given data:
A step-down transformer with 125 loops on the secondary side. The voltage at the primary side is
Formula used:
The expression for power at the input side is written as,
Here,
The expression for power at the output side is written as,
Here,
Explanation:
Consider the expression for the input power.
Substitute
Similarly, consider the expression for the output power.
Substitute
Conclusion:
Hence, the power at the input and the output side is same and is equal to
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