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.