The capacitance of a parallel plate capacitor:

$\overline{){\mathbf{C}}{\mathbf{=}}\frac{{\mathbf{\epsilon}}_{\mathbf{0}}\mathbf{A}}{\mathbf{d}}{\mathbf{=}}\frac{{\mathbf{k\epsilon}}_{\mathbf{0}}\mathbf{A}}{\mathbf{d}}}$

The charge stored on a capacitor:

$\overline{){\mathbf{Q}}{\mathbf{=}}{\mathbf{C}}{\mathbf{V}}}$

Energy stored by a capacitor:

$\overline{){\mathbf{U}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{C}}{{\mathbf{V}}}^{{\mathbf{2}}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{Q}}{\mathbf{V}}{\mathbf{=}}\frac{{\mathbf{Q}}^{\mathbf{2}}}{\mathbf{2}\mathbf{C}}}$

The electric field in a parallel plate capacitor:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{Q}}{{\mathbf{\epsilon}}_{\mathbf{0}}\mathbf{A}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{d}}}$

**(i)**

C_{0} = ε_{0}A/l

C = kε_{0}A/l

C/C_{0} = kε_{0}A/l ÷ ε_{0}A/l = k

Given a parallel-plate capacitor with plates of area A separated by a distance l. Consider the quantities, (i) capacitance C, (ii) magnitude E of the electric field between the plates, (iii) magnitude of the charge Q on the plates, (iv) potential difference ΔV between the plates, and (v) energy U stored in the capacitor

Assume we apply a given potential difference ΔV_{0} to the plates.

Suppose we had not changed the geometry of the capacitor but had filled the space between the plates with a dielectric of dielectric constant, K but instead of keeping Q constant we keep the potential difference ΔV_{0} constant. How would that affect the quantities (i) - (v)?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Energy Stored by Capacitor concept. You can view video lessons to learn Energy Stored by Capacitor. Or if you need more Energy Stored by Capacitor practice, you can also practice Energy Stored by Capacitor practice problems.