Question

learning goal: to review the meaning of capacitance and ways of changing the capacitance of a parallel - plate capacitor. capacitance is one of the central concepts in electrostatics. understanding its meaning and the difference between its definition and the ways of calculating capacitance can be challenging at first. this tutorial is meant to help you become more comfortable with capacitance. recall the fundamental formula for capacitance c = q/δvc, where c is the capacitance in farads, q is the charge stored on the plates in coulombs, and δvc is the potential difference (or voltage) between the plates. in the following problems it may help to keep in mind that the voltage is related to the strength of the electric field e and the distance between the plates, d, by δvc = ed. part b consider an air - filled charged capacitor. how can its capacitance be increased? view available hint(s) increase the charge on the capacitor. decrease the charge on the capacitor. increase the spacing between the plates of the capacitor. decrease the spacing between the plates of the capacitor. increase the length of the wires leading to the capacitor plates. submit part c

Explanation:

Step1: Recall capacitance formula

For a parallel - plate capacitor, $C=\frac{\epsilon_0A}{d}$, where $\epsilon_0$ is the permittivity of free space, $A$ is the area of the plates and $d$ is the distance between the plates. Also, $C = \frac{Q}{\Delta V_C}$.

Step2: Analyze each option

• Increasing the charge $Q$ on the capacitor while $\Delta V_C$ changes proportionally (since $C=\frac{Q}{\Delta V_C}$) does not change the capacitance $C$ itself.
• Decreasing the charge on the capacitor also does not change the capacitance as it is a property of the capacitor's structure.
• Increasing the spacing $d$ between the plates according to $C=\frac{\epsilon_0A}{d}$ will decrease the capacitance.
• Decreasing the spacing $d$ between the plates according to $C=\frac{\epsilon_0A}{d}$ will increase the capacitance.
• The length of the wires leading to the capacitor plates has no effect on the capacitance of the parallel - plate capacitor.

Answer:

Decrease the spacing between the plates of the capacitor.