A parallel plate capacitor is constructed from two square...

A parallel plate capacitor is constructed from two square conducting plates of length $L=0.10 \mathrm{m}$ on a side. There is air between the plates, which are separated by a distance $d=89 \mu \mathrm{m} .$ The capacitor is connected to a $10.0 \mathrm{V}$ battery. (a) After the capacitor is fully charged, what is the charge on the upper plate? (b) The battery is disconnected from the plates, and the capacitor is discharged through a resistor $R=0.100 \mathrm{M} \Omega .$ Sketch the current through the resistor as a function of time $t(t=0$ corresponds to the time when $R$ is connected to the capacitor). (c) How much energy is dissipated in $R$ over the whole discharging process?

A parallel plate capacitor is constructed from two square conducting plates of length $L=0.10 \mathrm{m}$ on a side. There is air between the plates, which are separated by a distance $d=89 \mu \mathrm{m} .$ The capacitor is connected to a $10.0 \mathrm{V}$ battery.
(a) After the capacitor is fully charged, what is the charge on the upper plate? (b) The battery is disconnected from the plates, and the capacitor is discharged through a resistor $R=0.100 \mathrm{M} \Omega .$ Sketch the current through the resistor as a function of time $t(t=0$ corresponds to the time when $R$ is connected to the capacitor).
(c) How much energy is dissipated in $R$ over the whole discharging process?

Key Concepts

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the expression U = ½CV², where C is the capacitance and V is the voltage across the capacitor. This stored energy is released or dissipated, for instance, as heat in a resistor during a discharge process, linking the energy storage and energy dissipation concepts in electrical circuits.

RC Circuit Discharge

An RC circuit consists of a resistor and a capacitor in series, which demonstrates an exponential decay of voltage, current, and charge over time when the capacitor discharges. The time-dependent behavior is characterized by the time constant ? = RC, which indicates how quickly the circuit will discharge.

Exponential Decay

Exponential decay in the context of RC circuits describes how quantities like charge and current decrease over time according to an exponential function. This mathematical concept is vital for predicting the behavior of circuits during transient events such as charging or discharging processes.

Parallel Plate Capacitor

A parallel plate capacitor is a device that stores electric charge and energy between two conductive plates separated by an insulating material. Its capacitance depends directly on the area of the plates and the permittivity of the dielectric, while being inversely proportional to the distance between the plates. This concept is fundamental in understanding how capacitors work in various electrical circuits.

Capacitance Calculation

The capacitance of a capacitor, defined as the ratio of charge stored to the applied voltage, is computed using the formula C = ??A/d for a parallel plate configuration, where ?? is the permittivity of free space, A is the plate area, and d is the separation between the plates. This calculation is crucial for determining how much charge is stored for a given voltage.

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