The potential difference between a pair of oppositely...

The potential difference between a pair of oppositely charged parallel plates is $400 \mathrm{V}$ a. If the spacing between the plates is doubled without altering the charge on the plates, what is the new potential difference between the plate? b. If the plate spacing is doubled while the potential difference between the plates is kept constant, what is the ratio of the final charge on one of the plates to the original charge?

The potential difference between a pair of oppositely charged parallel plates is $400 \mathrm{V}$
a. If the spacing between the plates is doubled without altering the charge on the plates, what is the new potential difference between the plate?
b. If the plate spacing is doubled while the potential difference between the plates is kept constant, what is the ratio of the final charge on one of the plates to the original charge?

Key Concepts

Relationship between Charge, Capacitance, and Voltage (Q = CV)

This fundamental equation, Q = CV, connects the three key quantities of a capacitor. It indicates that for a fixed charge, changes in capacitance (due to changes in geometry) will inversely affect the potential difference. Conversely, if the voltage is held constant while modifying the capacitance, the stored charge must change proportionally.

Charge Conservation in Isolated Systems

In an isolated capacitor, the total charge on the plates remains constant even if the physical parameters of the capacitor are changed. This principle is crucial when analyzing situations where modifications such as doubling the spacing between the plates are made without adding or removing charge.

Potential Difference

The potential difference across a capacitor is the voltage difference between its two plates. For a given stored charge, the voltage is given by V = Q/C. Thus, if the capacitance is altered by a physical change, such as changing the plate spacing, the voltage will adjust accordingly when the charge remains constant.

Capacitance

Capacitance is a measure of a capacitor’s ability to store electric charge per unit potential difference. In a parallel plate capacitor, capacitance is defined by the formula C = ??A/d, where ?? is the permittivity of free space, A is the area of the plates, and d is the separation between them. Any change to the physical separation between the plates directly affects the capacitance, with an increased separation resulting in a reduced capacitance.

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