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 don't even know what formulas to use

All of these questions can be answered by using the same formula.

C = (epsilon)*A/d ,

where 'epsilon' is the permittivity of the dielectric between the plates.

If there is air or vacuum between the plates, use
epsilon0 = 8.85*10^-12 farads/meter

A is the plate are and d is the plate separation. Use meters.

To find the radius of the plates in a parallel-plate capacitor, you can use the formula for capacitance:

C = (ε₀ * A) / d,

where C is the capacitance, ε₀ is the permittivity of free space, A is the area of one plate, and d is the separation between the plates.

1. To find the radius of the plates if the capacitance is 1.1 uF, you need to rearrange the formula to solve for the radius:

C = (ε₀ * π * R²) / d,

where π is the mathematical constant pi.

Now, rearranging the formula:

R² = (C * d) / (ε₀ * π).

Substituting the given values:

R² = (1.1 * 10⁻⁶ F * 1.2 * 10⁻³ m) / (8.85 * 10⁻¹² F/m * π).

By calculating this expression, you can find the value of R². To find the radius R, take the square root of R². Thus, the answer to the first question is the square root of the expression above.

2. If the separation between the plates is increased while maintaining a capacitance of 1.1 uF, the radius of the plates should be increased. This is because the capacitance of a parallel-plate capacitor is proportional to the area of the plates (C = (ε₀ * A) / d). By increasing the separation between the plates, the area of each plate remains the same, so the radius must be increased to achieve the desired capacitance.

3. To find the radius of the plates for a plate separation of 3.4 mm, you can use the same formula as in question 1, but with the given separation distance:

R² = (1.1 * 10⁻⁶ F * 3.4 * 10⁻³ m) / (8.85 * 10⁻¹² F/m * π).

By calculating this expression, you can find the value of R². To find the radius R, take the square root of R². Thus, the answer to the third question is the square root of the expression above.