Question

When operated on a household 110.0-V line, typical hair dryers draw about 1650 W of power. We can model the current as a long straight wire in the handlé. During use, the current is about 1.85 cm from the user's hand. What is the current in the dryer? Number What is the resistance of the dryer? Number What magnetic field does the dryer produce at the user's hand?

Answer 1

Answer:

Current = 15 A

Resistance = 7.33 ohm

Magnetic field = 1.62 x 10^-4 Tesla

Explanation:

V = 110 V, P = 1650 W, r = 1.85 cm,

(a) Let i be the current

P = V x i

i = 1650 / 110 = 15 A

(b) Let R be the resistance

V = i R

R = 110 / 15 = 7.33 Ohm

(c) Let B be the magnetic field

B = μ0 / 4π x 2i / r

B = 10^-7 x 2 x 15 / 0.0185 = 1.62 x 10^-4 Tesla

Answer 2

The current in the dryer is 15 A.

The resistance of the dryer is 7.33 ohms

The magnetic field the dryer produced at the user's hand is 1.62 x 10⁻⁴ T.

Current in the dryer

The current in the dryer is calculated as follows;

I = P/V

I = 1650/110

I = 15 A

Resistance of the dryer

The resistance of the dryer is calculated as follows;

R = V/I

R = 11O/15

R = 7.33 ohms

Magnetic field produced by the dryer

$B = \frac{\mu_0 I}{2\pi r} \\\\B = \frac{4\pi \times 10^{-7} \times 15}{2\pi \times 0.0185} \\\\B = 1.62 \times 10^{-4} \ T$

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