The generator at a power plant produces AC at 24,000 V. A transformer steps this up to 345,000 V for transmission over power lines. If there are 2,000 turns of wire in the input coil of the transformer, how many turns must there be in the output coil?
For transformers, the turns ratio equals the voltage ratio.
2000/n = 24,000/345,000
Solve for n.
To determine the number of turns in the output coil, we can use the formula for transformer turns ratio:
Turns ratio = Output voltage / Input voltage
Given that the input voltage is 24,000 V and the output voltage is 345,000 V, we can calculate the turns ratio:
Turns ratio = 345,000 V / 24,000 V = 14.375
Since the turns ratio represents the ratio between the number of turns in the output coil and the number of turns in the input coil, we can express this as:
Number of turns in output coil / Number of turns in input coil = Turns ratio
Simplifying the equation, we get:
Number of turns in output coil = Turns ratio x Number of turns in input coil
Substituting the values we have, we get:
Number of turns in output coil = 14.375 x 2,000
Number of turns in output coil = 28,750
Therefore, there must be 28,750 turns in the output coil.
To determine the number of turns in the output coil of the transformer, we can use the equation:
V1/N1 = V2/N2
Where:
- V1 is the voltage in the input coil (24,000 V)
- N1 is the number of turns in the input coil (2,000 turns)
- V2 is the desired voltage in the output coil (345,000 V)
- N2 is the number of turns in the output coil (unknown)
Rearranging the equation, we can solve for N2:
N2 = (V2 * N1) / V1
Plugging in the values:
N2 = (345,000 V * 2,000 turns) / 24,000 V
Calculating:
N2 = 28,750 turns
Therefore, there should be approximately 28,750 turns in the output coil of the transformer.