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Chapter 30: Problem 55

A transformer contains a primary coil with 200 turns and a secondary coil with 120 turns. The secondary coil drives a current \(I\) through a \(1.00-\mathrm{k} \Omega\) resistor. If an input voltage \(V_{\mathrm{rms}}=75.0 \mathrm{~V}\) is applied across the primary coil, what is the power dissipated in the resistor?

Short Answer

Expert verified
Question: Calculate the power dissipated in a \(1.00-\mathrm{k}\Omega\) resistor connected to the secondary coil of a transformer when the primary coil has an input voltage of \(75.0\mathrm{V}\). The primary coil has 200 turns, and the secondary coil has 120 turns. Answer: The power dissipated in the resistor is \(2.025\mathrm{W}\).

Step by step solution

01

Determine the turns ratio

To find the turns ratio in the transformer, we will divide the number of turns on the secondary coil (\(N_S\)) by the number of turns on the primary coil (\(N_P\)): \(n = \frac{N_S}{N_P}\) \(n = \frac{120}{200} = 0.6\)
02

Calculate the output voltage

Using the transformer turns ratio, we can find the output voltage (\(V_{out}\)) using the input voltage (\(V_{in}\)): \(V_{out} = n \times V_{in}\) \(V_{out} = 0.6 \times 75.0 \mathrm{V} = 45.0\mathrm{V}\)
03

Use Ohm's Law to find the current

With the output voltage and the resistance value, we can use Ohm's Law to find the current (\(I\)) through the \(1.00-\mathrm{k}\Omega\) resistor: \(I = \frac{V_{out}}{R}\) \(I = \frac{45.0\mathrm{V}}{1.00\mathrm{k}\Omega} = 0.045\mathrm{A}\)
04

Calculate the power dissipated in the resistor

Finally, we can find the power dissipated in the resistor (\(P\)) using the formula \(P = I^2R\): \(P = I^2R\) \(P = (0.045\mathrm{A})^2 \times 1.00\mathrm{k}\Omega = 2.025\mathrm{W}\) Therefore, the power dissipated in the resistor is \(2.025\mathrm{W}\).

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