A parallel-plate capacitor is constructed from two circular metal plates or radius R. The plates are separated by a distance of 1.2mm.
1. What radius must the plates have if the capacitance of this capacitor is 1.1 uF?
2. If the separation between the plates is increased, should the radius of the plates be increased or decreased to maintain a capacitance of 1.1 uF. Explain.
3. Find the radius of the plates that gives a capacitance of 1.1 uF for a plate separation of 3.4 mm.
I will be happy to crituque your work.
I don't know what formulas to use
To answer these questions, we need to use the formula for the capacitance of a parallel-plate capacitor:
C = (ε₀ * A) / d
where C is the capacitance, ε₀ is the vacuum permittivity (a constant), A is the area of the plates, and d is the separation between the plates.
Let's solve each question step by step:
1. To find the radius of the plates for a capacitance of 1.1 uF, we need to rearrange the formula as follows:
C = (ε₀ * π * R²) / d
Solving for R:
R² = (C * d) / (ε₀ * π)
R = √((C * d) / (ε₀ * π))
Plugging in the values:
R = √((1.1 * 10^(-6) * 1.2 * 10^(-3)) / (8.85 * 10^(-12) * 3.14))
Calculating the value of R will provide the answer to the first question.
2. If the separation between the plates is increased, and we want to maintain a capacitance of 1.1 uF, we need to adjust the radius of the plates. From the formula for capacitance, we can see that the capacitance is directly proportional to the area of the plates (A) and inversely proportional to the separation between the plates (d). Since the radius (R) affects the area (A), we can conclude that if the separation is increased, the radius of the plates should be increased as well to maintain the same capacitance.
3. For the third question, we need to determine the radius that gives a capacitance of 1.1 uF for a plate separation of 3.4 mm. We can use the same formula as in the first question:
R = √((C * d) / (ε₀ * π))
Plugging in the given values:
R = √((1.1 * 10^(-6) * 3.4 * 10^(-3)) / (8.85 * 10^(-12) * 3.14))
Solving for R will give us the desired radius for this specific scenario.