Question

A clothes dryer has a resistance of 50.0 Ω and operates on 110.0 V. How many joules of energy is provided by the clothes dryer in 10.0 s?
Group of answer choices

12,000 joules

1,210 joules

2,420 joules

4,840 joules

Answer 1

To determine the energy provided by the clothes dryer, we first need to calculate the power (in watts) it uses. Power can be calculated using Ohm's Law and the formula for electrical power:

\[
P = \frac{V^2}{R}
\]

Where:
- \( P \) is the power in watts
- \( V \) is the voltage in volts
- \( R \) is the resistance in ohms

Given:
- \( V = 110.0 \, \text{V} \)
- \( R = 50.0 \, \Omega \)

Substituting the values into the formula:

\[
P = \frac{(110.0)^2}{50.0}
\]

Calculating \( 110.0^2 \):

\[
110.0^2 = 12100 \, \text{V}^2
\]

Now substituting back:

\[
P = \frac{12100}{50.0} = 242 \, \text{W}
\]

Now that we have the power in watts, we can calculate the total energy provided by the clothes dryer over 10.0 seconds using the formula for energy:

\[
E = P \times t
\]

Where:
- \( E \) is the energy in joules
- \( P \) is the power in watts
- \( t \) is time in seconds

Given that \( t = 10.0 \, \text{s} \):

\[
E = 242 \, \text{W} \times 10.0 \, \text{s} = 2420 \, \text{J}
\]

Thus, the energy provided by the clothes dryer in 10.0 seconds is **2,420 joules**.

Answer choice: **2,420 joules**.