To determine the resistance of a device when given the voltage and current, we can use Ohm's Law. Ohm's Law states that the resistance [tex]\( R \)[/tex] in a circuit can be calculated using the formula:
[tex]\[ V = I \cdot R \][/tex]
where:
- [tex]\( V \)[/tex] is the voltage across the device,
- [tex]\( I \)[/tex] is the current flowing through the device,
- [tex]\( R \)[/tex] is the resistance of the device.
We are given:
- Voltage ([tex]\( V \)[/tex]) = 81 V
- Current ([tex]\( I \)[/tex]) = 3 A
We need to find the resistance [tex]\( R \)[/tex]. Rearranging Ohm's Law to solve for [tex]\( R \)[/tex], we get:
[tex]\[ R = \frac{V}{I} \][/tex]
Substituting the given values for voltage and current:
[tex]\[ R = \frac{81 \, \text{V}}{3 \, \text{A}} \][/tex]
[tex]\[ R = 27 \, \Omega \][/tex]
Therefore, the resistance of the device is [tex]\( 27 \, \Omega \)[/tex].
The best answer is:
D. [tex]$27 \Omega$[/tex]
