Capacitor X of capacitance C has square plates of side length l and separation d and is made with a dielectric of relative permittivity ε - AQA - A-Level Physics - Question 19 - 2022 - Paper 2

To find the capacitance of capacitor Y, we can use the formula for the capacitance of a parallel plate capacitor:

C = rac{εA}{d}

where:

• $C$ is the capacitance,
• $ε$ is the permittivity of the dielectric,
• $A$ is the area of the plates, and
• $d$ is the separation between them.

For capacitor X:

• Capacitance: $C_X = C$
• Area: $A_X = l^2$
• Separation: $d_X = d$
• Dielectric: $ε_X = ε$

Thus, we can write: C_X = rac{ε l^2}{d}

For capacitor Y:

• Area: $A_Y = (3l)^2 = 9l^2$
• Separation: d_Y = rac{d}{3}
• Dielectric: ε_Y = rac{ε}{3}

Now we can substitute these values into the capacitance formula for capacitor Y:

C_Y = rac{ε_Y A_Y}{d_Y} = rac{rac{ε}{3} imes 9l^2}{rac{d}{3}}

Simplifying this gives: C_Y = rac{ε imes 9l^2}{3} imes rac{3}{d} = rac{9ε l^2}{d}

Now, since we know that: C_X = rac{ε l^2}{d}

This implies that: $C_Y = 9C_X = 9C$

Thus, the capacitance of Y is:

Answer: 9C