Thank you for visiting A parallel plate capacitor has circular plates with a radius of 7 54 cm and a separation of 1 71 mm a Calculate the capacitance. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To calculate the capacitance of a parallel-plate capacitor and the charge on its plates when a potential difference is applied, we'll follow these steps:
(a) Calculate the capacitance.
The capacitance [tex]C[/tex] of a parallel-plate capacitor is given by the formula:
[tex]C = \frac{\varepsilon_0 \cdot A}{d}[/tex]
Where:
- [tex]\varepsilon_0[/tex] is the vacuum permittivity, approximately [tex]8.85 \times 10^{-12} \ \text{F/m}[/tex].
- [tex]A[/tex] is the area of one of the plates.
- [tex]d[/tex] is the separation between the plates.
Calculate the area [tex]A[/tex]: The plates are circular, so the area [tex]A[/tex] is:
[tex]A = \pi r^2[/tex]
With [tex]r = 7.54 \ \text{cm} = 0.0754 \ \text{m}[/tex]:
[tex]A = \pi (0.0754)^2
\approx 0.0179 \ \text{m}^2[/tex]Plug the known values into the formula:
The separation [tex]d = 1.71 \ \text{mm} = 0.00171 \ \text{m}[/tex].
[tex]C = \frac{(8.85 \times 10^{-12} \ \text{F/m}) \times 0.0179 \ \text{m}^2}{0.00171 \ \text{m}}
\approx 9.25 \times 10^{-12} \ \text{F} \text{ or } 9.25 \ \text{pF}[/tex]
(b) What charge will appear on the plates if a potential difference of 97.7 V is applied?
The charge [tex]Q[/tex] on the plates is related to the capacitance and the potential difference [tex]V[/tex] by the formula:
[tex]Q = C \cdot V[/tex]
Using the capacitance we calculated:
[tex]Q = (9.25 \times 10^{-12} \ \text{F}) \times 97.7 \ \text{V}
\approx 9.03 \times 10^{-10} \ \text{C} \text{ or } 903 \ \text{pC}[/tex]
So, the capacitance of the capacitor is approximately [tex]9.25 \ \text{pF}[/tex], and the charge on the plates when a [tex]97.7 \ \text{V}[/tex] potential difference is applied is approximately [tex]903 \ \text{pC}[/tex].
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