A resistor has a voltage drop of 18 V and carries a current of 3 A. What is its resistance?
6 Ω
To determine the resistance of a resistor, we use Ohm's Law, which states that the voltage across a resistor is equal to the product of the current flowing through it and its resistance. The formula is given as:
\(V = I \times R\)
Where:
- \(V\) is the voltage drop (volts, V).
- \(I\) is the current (amperes, A).
- \(R\) is the resistance (ohms, Ω).
We are given:
- Voltage drop, \(V = 18 \, \text{V}\)
- Current, \(I = 3 \, \text{A}\)
We need to find the resistance \(R\). Rearranging the formula to solve for \(R\) gives:
\(R = \frac{V}{I}\)
Substituting the given values:
\(R = \frac{18 \, \text{V}}{3 \, \text{A}} = 6 \, \Omega\)
Therefore, the resistance of the resistor is 6 Ω.
Let's verify the options to explain why 6 Ω is correct:
- 15 Ω - Substituting into the formula gives a voltage drop of \(45 \, \text{V}\), which does not match the given \(18 \, \text{V}\).
- 1/6 Ω - Substituting into the formula gives a voltage drop of \(0.5 \, \text{V}\), insufficient for \(18 \, \text{V}\).
- 54 Ω - Substituting into the formula gives a voltage drop of \(162 \, \text{V}\), which is too high.
Hence, the correct answer is indeed 6 Ω.
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