A label on a hair dryer reads "110V \(1250 \mathrm{~W}\)." What is the peak current in the hair dryer, assuming that it behaves like a resistor?

Short Answer

Expert verified
Answer: The peak current in the hair dryer is 16.06 A.

Step by step solution

01

Find effective (root mean square) current

Using the power equation, we can find the effective (RMS) current: \(P = IV\) \(I_{rms} = \frac{P}{V}\) Plug in the given values for power and voltage: \(I_{rms} = \frac{1250 \mathrm{~W}}{110 \mathrm{~V}}\) Calculate the RMS current: \(I_{rms} = 11.36 \mathrm{~A}\)
02

Find the resistance

Now, we will use Ohm's Law to find the resistance of the hair dryer: \(V = IR\) \(R = \frac{V}{I}\) Plug in the given value for voltage and the calculated effective current: \(R = \frac{110 \mathrm{~V}}{11.36 \mathrm{~A}}\) Calculate the resistance: \(R = 9.68 \mathrm{~\Omega}\)
03

Find the peak current

Finally, we will use the peak current equation to find the peak current in the hair dryer: \(I_{peak} = I_{rms} \sqrt{2}\) Plug in the calculated RMS current: \(I_{peak} = 11.36 \mathrm{~A} \sqrt{2}\) Calculate the peak current: \(I_{peak} = 16.06 \mathrm{~A}\) So, the peak current in the hair dryer is \(16.06 \mathrm{~A}\).

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