PhysicsLAB: Test Scenario: Capacitor Circuit Scenario

This scenario is based on an APC E&M practice exam released in 2007.

Refer to the following information for the next nine questions.

A parallel plate capacitor, X, with plate area, A, and plate separation, d, is filled with air and charged by connecting the capacitor thorough a switch to a power supply of emf,

, as shown in the following diagram.

If the emf of the battery is 45 volts, determine an expression for the charge on each plate of capacitor X.

Which plate has a positive charge?

What is the direction of the electric field between the capacitor's plates?

Develop an expression for the amount of energy stored on capacitor X?

The switch is then flipped to the right, so that capacitor X is disconnected from the power supply and is instead connected to a second uncharged capacitor, Y. Capacitor Y has the same plate separation as capacitor X, but twice the plate area and is filled with mica having a dielectric constant of 7.

Calculate the equilibrium charges on each capacitor in terms of the original charge Q.

Calculate the voltage across X.

Does capacitor Y have the same final voltage as capacitor X?

Develop an expression for the amount of energy stored on capacitor Y.

Once charged, the two capacitors are disconnected from one another and a resistor R is connected across the two sides of capacitor Y which then discharges through the resistor.

In terms of physical constants, A, d, and R how much time passes before capacitor Y has only 37% of its original charge?