Multiple Choice
What is the capacitance of a parallel plate capacitor with plate area separated by a distance ?
26. Capacitors & Dielectrics
Parallel Plate Capacitors
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Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates?
A
2.23×10−8
B
2.23×10−10
C
2.23×10−11
D
2.23×10−12
Verified step by step guidance1
First, understand that the problem involves calculating the capacitance of a parallel plate capacitor. The formula for the capacitance \( C \) of a parallel plate capacitor is given by: \( C = \frac{\varepsilon_0 A}{d} \), where \( \varepsilon_0 \) is the permittivity of free space (approximately \( 8.85 \times 10^{-12} \text{ F/m} \)), \( A \) is the area of one of the plates, and \( d \) is the separation between the plates.
Calculate the area \( A \) of one of the circular plates. The area of a circle is given by \( A = \pi r^2 \), where \( r \) is the radius of the circle. Here, the radius \( r \) is 2 cm, which needs to be converted to meters (0.02 m).
Substitute the radius into the area formula: \( A = \pi (0.02)^2 \). Calculate this to find the area in square meters.
Convert the separation distance \( d \) from millimeters to meters. Since 5 mm is equal to 0.005 m, use this value for \( d \).
Substitute the values of \( \varepsilon_0 \), \( A \), and \( d \) into the capacitance formula: \( C = \frac{8.85 \times 10^{-12} \times A}{0.005} \). Simplify this expression to find the capacitance in farads.
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