The generator at a power plant produces AC at 24,000 V. A transformer steps this
up to 480,000 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?
Twenty times as many.
The voltage ration (2O) equals the turns ratio.
To solve this problem, we need to use the principle of voltage transformation in a transformer. The voltage ratio in a transformer is equal to the turns ratio. We can use the formula:
Voltage ratio = Turns ratio
In this case, the voltage ratio is the ratio of the output voltage to the input voltage, which is given as:
Voltage ratio = 480,000 V / 24,000 V = 20
The turns ratio is the ratio of the number of turns in the output coil to the number of turns in the input coil. Let's call the number of turns in the output coil N.
Turns ratio = N / 2,000
Using the voltage ratio formula, we can equate the two ratios:
Voltage ratio = Turns ratio
20 = N / 2,000
To find the value of N, we can rearrange the equation:
N = Voltage ratio * 2,000
Substituting the value of the voltage ratio:
N = 20 * 2,000
N = 40,000
Therefore, there must be 40,000 turns in the output coil.