Absolutely, let's go through the problem step-by-step to determine the power [tex]\( P \)[/tex] when [tex]\( E = 120 \, \text{V} \)[/tex] and [tex]\( R = 83 \, \Omega \)[/tex].
1. Understanding the Formula:
We are given the formula for power:
[tex]\[
P = \frac{E^2}{R}
\][/tex]
where [tex]\( P \)[/tex] is the power in watts (W), [tex]\( E \)[/tex] is the voltage in volts (V), and [tex]\( R \)[/tex] is the resistance in ohms (Ω).
2. Given Values:
We have:
[tex]\[
E = 120 \, \text{V}
\][/tex]
[tex]\[
R = 83 \, \text{Ω}
\][/tex]
3. Calculating [tex]\( E^2 \)[/tex]:
First, we compute [tex]\( E^2 \)[/tex]:
[tex]\[
E^2 = 120^2 = 14400 \, \text{V}^2
\][/tex]
4. Plugging Values into the Formula:
Next, substitute [tex]\( E^2 \)[/tex] and [tex]\( R \)[/tex] into the formula:
[tex]\[
P = \frac{14400 \, \text{V}^2}{83 \, \text{Ω}}
\][/tex]
5. Performing the Division:
[tex]\[
P = \frac{14400}{83} \approx 173.494 \, \text{W}
\][/tex]
After performing the division, we see that the power [tex]\( P \)[/tex] is approximately [tex]\( 173.494 \, \text{W} \)[/tex].
6. Converting to Kilowatts:
To convert watts to kilowatts, divide by 1000:
[tex]\[
P_{\text{kW}} = \frac{173.494 \, \text{W}}{1000} \approx 0.173 \, \text{kW}
\][/tex]
Given the results, let's match the value to the provided choices and round to three places as required:
- 1.73 W: This is not the correct value, as [tex]\( 173.494 \, \text{W} \)[/tex] is much higher.
- 14.5 kW: This is incorrect, as [tex]\( 14.5 \, \text{kW} \)[/tex] is far too high.
- 14.5 W: Again, this is incorrect as [tex]\( 173.494 \, \text{W} \)[/tex] is quite higher.
- 1.73 kW: This does not match, as [tex]\( 1.73 \, \text{kW} \)[/tex] is higher than [tex]\( 0.173 \, \text{kW} \)[/tex].
- 0.173 kW: This is the correct value, as calculated.
So, the correct choice is:
[tex]\[
\boxed{0.173 \, \text{kW}}
\][/tex]
