Tutorial 4A - Properties of Capacitors

Learning Objectives

• Recall that a capacitor is a charge store.

• Describe the properties of a capacitor.

• Recognise and use the equation Q = CV

• To explain how capacitors allow the passage of AC, but not DC.

Key Questions

How does a capacitor hold charge?

How can a capacitor allow AC to flow but block DC?

How can we show the relationship between charge and voltage?

### Resistive Circuits in AC

In simple AC circuits and DC circuits we have used resistive components.

If we draw a phasor diagram for the current and the voltage, we would see: In this diagram, the phase vectors would be on top of each other; they have been separated to make them clear.

In a simple resistive AC circuit, there is zero phase difference between the vectors, so we can ignore the phase term, f.   So we can write equations for the instantaneous voltages and currents at any time:  And here are the graphs that have been generated by these relationships.  You can see that they are in phase. We know that resistance is the opposition to the flow of current, and the resistance in this circuit remains constant whatever the frequency.

### Reactance

In AC circuits, there is another kind of opposition to the flow of current, called reactance.  There are two main components that have a reactance, which is frequency dependent.  The reactance in a capacitor is the opposition to the change in voltage across the capacitor.  The reactance in an inductor is the opposition to the change in current through the inductor.  There is no reactance in purely resistive components.

Reactance is dependent on the frequency.

To make sense of reactance, we need to know something about the capacitor and the inductor.  We will look at the capacitor in this tutorial and the inductor in the next tutorial.

### Properties of Capacitors

Capacitors are short term charge stores that hold electrical energy in the form of an electric field. They are used widely in electronic circuits. They are at the heart of all electronic timing devices. They also can act as back up power supplies to memory chips. Another use is to smooth out the ripples from a power supply; in effect they are electrical springs. They are also found in oscillators, signal generators, tone controls (filter circuits) to name a few. A variable capacitor is used to tune radios.

At its simplest a capacitor consists of two metal plates separated by a layer of insulating material called a dielectric.  The picture to the right shows some different types of capacitor.  Capacitance is measured in units called farads (F). A farad is a very big unit, and we are much more likely to use microfarads (mF) or nanofarads (nF). You may even see picofarads (pF)

• 1 mF = 1 × 10-6 F

• 1 nF = 1 × 10-9 F

• 1 pF = 1 × 10-12 F

The symbol for a capacitor is shown below: There are two types of capacitor, electrolytic and non-electrolytic.

• Electrolytic capacitors hold much more charge

• Electrolytic capacitors have to be connected with the correct polarity, otherwise they can explode.

The properties of electrolytic and non-electrolytic capacitors are summed up on this table:

 Electrolytic Non electrolytic Advantages: High capacitance Can have high working voltages. Advantages: Do not lose charge Polarity does not matter Stable up to 106 Hz (or more) Disadvantages: Polarity important High leakage current Not stable above 10 kHz Can be damaged by AC Disadvantages: Low capacitance

Question 1

 Convert these value of capacitors: 1 pF =                                                   F 4.7 mF =                                                F 1200 pF =                                             F  =                                                   nF 3.2 × 10-6  F =                                      mF =                                                   nF 4.7 mF =                                              mF Question 2

Why is an electrolytic capacitor likely to be damaged by AC? ### How a capacitor holds charge

Capacitance is defined as:

The charge required to cause unit potential difference in a conductor.

Capacitance is measured in units called farads (F) of which the definition is:

1 Farad is the capacitance of a conductor, which has potential difference of 1 volt when it carries a charge of 1 coulomb.

So we can write from this definition:

Capacitance (F) = Charge (C)

Voltage (V)

In code, this is written:

C = Q

C

[Q - charge in coulombs (C); C – capacitance in farads (F); V - potential difference in volts (V)]

We can show the relationship between the voltage and the charge on the graph. The charge is directly proportional to the current. This means that it's a straight line with a positive gradient, going through the origin.

Capacitance is the gradient of the graph.

The voltage rises as we charge up a capacitor, and falls as the capacitor discharges. The current falls from a high value as the capacitor charges up, and falls as it discharges. If we connect a capacitor in series with a bulb:

• If connected to a d.c. circuit, the bulb flashes, then goes out.

• In an a.c. circuit, the bulb remains on. The capacitor does NOT conduct electricity. The "flow" of a.c. is due to the charge and discharge of the capacitor.

 Explain how the graph shows that voltage and charge are directly proportional. Question 4 Why does a capacitor appear to allow ac to flow, but not dc? Question 5 What is the charge held by a 470 microfarad capacitor charged to a p.d. of 8.5 V? 