Question
The potential difference between two parallel wires in air is 120 V. They hold equal and opposite charges of 3.5x10^-13C. What is the capacitance of the two wires?
Group of answer choices
3.25x10^-7 F
4.25x10^-6 F
2.92x10^-26 F
3.4x10^-26 F
Group of answer choices
3.25x10^-7 F
4.25x10^-6 F
2.92x10^-26 F
3.4x10^-26 F
Answers
Answered by
GPT-4o mini
The capacitance \( C \) of a capacitor can be calculated using the formula:
\[
C = \frac{Q}{V}
\]
where:
- \( C \) is the capacitance in farads (F),
- \( Q \) is the charge stored in coulombs (C),
- \( V \) is the potential difference in volts (V).
In this case:
- \( Q = 3.5 \times 10^{-13} \) C (the charge on one of the wires),
- \( V = 120 \) V (the potential difference between the wires).
Using the formula:
\[
C = \frac{3.5 \times 10^{-13} \text{ C}}{120 \text{ V}}
\]
Calculating this gives:
\[
C = \frac{3.5 \times 10^{-13}}{120} = 2.91667 \times 10^{-15} \text{ F}
\]
Rounding this to three significant figures results in:
\[
C \approx 2.92 \times 10^{-15} \text{ F}
\]
However, the available answer choices do not match this result. It's essential to double-check the computations and ensure the question's inputs align correctly. Investigating shows that the final capacitance of \( 2.92 \times 10^{-15} \) F does not find a corresponding option in the list provided. This discrepancy suggests that it is something outside of possible answers or a miscommunication in values.
Nevertheless, based on our calculations and using the charge and voltage provided, the capacitance derived is distinctly \( 2.92 \times 10^{-15} \) F. If the available choices are interpreted correctly, it would imply a procedure alteration or an error in provided values.
\[
C = \frac{Q}{V}
\]
where:
- \( C \) is the capacitance in farads (F),
- \( Q \) is the charge stored in coulombs (C),
- \( V \) is the potential difference in volts (V).
In this case:
- \( Q = 3.5 \times 10^{-13} \) C (the charge on one of the wires),
- \( V = 120 \) V (the potential difference between the wires).
Using the formula:
\[
C = \frac{3.5 \times 10^{-13} \text{ C}}{120 \text{ V}}
\]
Calculating this gives:
\[
C = \frac{3.5 \times 10^{-13}}{120} = 2.91667 \times 10^{-15} \text{ F}
\]
Rounding this to three significant figures results in:
\[
C \approx 2.92 \times 10^{-15} \text{ F}
\]
However, the available answer choices do not match this result. It's essential to double-check the computations and ensure the question's inputs align correctly. Investigating shows that the final capacitance of \( 2.92 \times 10^{-15} \) F does not find a corresponding option in the list provided. This discrepancy suggests that it is something outside of possible answers or a miscommunication in values.
Nevertheless, based on our calculations and using the charge and voltage provided, the capacitance derived is distinctly \( 2.92 \times 10^{-15} \) F. If the available choices are interpreted correctly, it would imply a procedure alteration or an error in provided values.