# 6.1.3: Summary

The capacitor is a device that is used to store electric charge. Capacitance, C, is measured in farads, F. The idealized device consists of two conductive plates separated by some distance, that space being filled by an insulating dielectric. Capacitance is directly proportional to the plate area and the dielectric's permittivity, and inversely proportional to the plate distance. Another important characteristic of the dielectric is its breakdown strength. Along with the plate spacing, this will establish the capacitor's voltage rating. The permittivity will also help to determine the capacitor's volumetric efficiency, a measure of how much capacitance can be achieved within a given volume. Non-ideal parameters include the ESR, or equivalent series resistance, which is ideally zero; and the effective parallel leakage resistance, ideally infinity. Absolute accuracy, temperature stability and similar parameters round out the distinguishing features of one kind of capacitor against another. When placed in parallel, capacitors add in the same manner as resistors in series. When placed in series, capacitors behave like resistors in parallel.

Perhaps the most important operational characteristic regarding capacitors is that voltage across a capacitor cannot change instantaneously. It will take some finite amount of time before the charge on the capacitor builds, leading to a predictable rise in voltage across it. Because of this, for DC circuits capacitors initially behave like shorts, but after sufficient time has passed, they behave like opens. The amount of time required to reach steady-state is five time constants, where one time constant is defined as the product of the circuit's effective resistance and its capacitance. The current charge curve is of the shape $$\varepsilon^{−t}$$. The current starts at a maximum and eventually approaches zero as time passes. The corresponding voltage shape is of the form $$1 - \varepsilon^{−t}$$. Here, the capacitor's voltage starts at zero and rises to some maximum value. The capacitor's voltage discharge curve effectively is swapped compared to the charge curve (e.g. voltage follows $$\varepsilon^{−t}$$).

## Review Questions

1. What are the physical characteristics of capacitors and how do they affect capacitance?

2. Define the voltage-current characteristic for capacitors.

3. What is meant by a capacitor's volumetric efficiency?

4. How do the permittivity and breakdown strength of the dielectric affect the overall capacitance and voltage rating?

5. How do capacitors combine when placed in series and how do they combine when placed in parallel?

6. Define the initial and steady-state behavior of capacitors.

7. Define time constant for an RC circuit.

8. Describe the charge and discharge characteristics of RC circuits.