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IP Consider a parallel-plate capacitor constructed from
Chapter 20, Problem 56P(choose chapter or problem)
Problem 56P
IP Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates arc separated by a distance of 1.5 mm. (a) What radius must the plates have if the capacitance of this capacitor is to be 1.0 μF? (b) If the separation between the plates is increased, should the radius of the plates be increased or decreased to maintain a capacitance of 1.0 μF? Explain, (c) Find the radius of the plates that gives a capacitance of 1.0 μF for a plate separation of 3.0 mm.
Questions & Answers
QUESTION:
Problem 56P
IP Consider a parallel-plate capacitor constructed from two circular metal plates of radius R. The plates arc separated by a distance of 1.5 mm. (a) What radius must the plates have if the capacitance of this capacitor is to be 1.0 μF? (b) If the separation between the plates is increased, should the radius of the plates be increased or decreased to maintain a capacitance of 1.0 μF? Explain, (c) Find the radius of the plates that gives a capacitance of 1.0 μF for a plate separation of 3.0 mm.
ANSWER:
Step 1 of 3:-
a)
Here we have to calculate the radius of the circular plates of the capacitor.
The area of the plate is,
.
The separation between the plates is,
.
The capacitance of the capacitor is,
.
The gap between the plates is filled with air and the permittivity of air is,
Now, we know that,
------------(1)
So, the radius of the plate is 7.34 m.