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When a device is used in a circuit with a voltage of 81 V and a current of 3 A, what is the resistance of the device?

A. 40.5 A
B. 243 A
C. [tex]$243 \Omega$[/tex]
D. [tex]$27 \Omega$[/tex]


Sagot :

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]