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The potential difference between two parallel wires in air is [tex]$120 V[tex]$[/tex]. They hold equal and opposite charges of [tex]$[/tex]7.5 \times 10^{-10} C$[/tex]. What is the capacitance of the two wires?

A. [tex]3.25 \times 10^{-7} F[/tex]
B. [tex]3.4 \times 10^{-26} F[/tex]
C. [tex]4.25 \times 10^{-6} F[/tex]
D. [tex]6.25 \times 10^{-12} F[/tex]



Answer :

GinnyAnswer
Sure! Let's solve this step by step.

1. Understanding the given values:
- The potential difference (V) between the two wires is \(120\, \text{V}\).
- The charge (Q) on the wires is \(7.5 \times 10^{-10}\, \text{C}\), wherein they hold equal and opposite charges.

2. Applying the formula for capacitance:
- The capacitance (C) of a system can be calculated using the formula:
[tex]\[ C = \frac{Q}{V} \][/tex]
- Here, \(Q\) is the charge and \(V\) is the potential difference.

3. Substitute the given values into the formula:
- \(Q = 7.5 \times 10^{-10} \text{ C}\)
- \(V = 120 \text{ V}\)

Substituting these:
[tex]\[ C = \frac{7.5 \times 10^{-10} \text{ C}}{120 \text{ V}} = 6.25 \times 10^{-12} \text{ F} \][/tex]

4. Comparing with the multiple-choice options:
- Now, we compare the calculated capacitance \(6.25 \times 10^{-12} \text{ F}\) with the given options:
- \(3.25 \times 10^{-7} \text{ F}\)
- \(3.4 \times 10^{-26} \text{ F}\)
- \(4.25 \times 10^{-6} \text{ F}\)
- \(6.25 \times 10^{-12} \text{ F}\)

- The correct match is \(6.25 \times 10^{-12} \text{ F}\).

Therefore, the capacitance of the two wires is [tex]\(\boxed{6.25 \times 10^{-12} \text{ F}}\)[/tex].

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