Capacitor Charge and Discharge

Introduction

A capacitor is an electronic component that can store a certain amount of charge. It has a value called its capacitance, measured in farads (which is a huge unit; we normally deal with microfarads or even picofarads). The capacitance is the amount of charge a capacitor can store per volt.

• Question: How much charge can a 100μF capacitor store at 6V?

It is an extremely useful device with many applications. For example, it can smooth a power supply’s output, or store the charge needed to power a photographic flash (a battery may not be able to deliver the necessary power over the short time period of a flash, but it can trickle charge a capacitor, which can then release the stored charge in one short burst).

This experiment allows you to discover how a capacitor charges and discharges when placed in a circuit. The circuit has a power supply, a resistor, the capacitor, and a two-way switch that can be set to either charge or discharge the capacitor. An ammeter in series with the capacitor monitors the current flowing in or out of the capacitor, and a voltmeter connected in parallel with the capacitor monitors the voltage across it.

The objective

To establish the relationship between time and the voltage for a capacitor that is charging or discharging.

The apparatus

You will need:

• Two multimeters

• A direct current (DC) power supply

• A breadboard

• A C=capacitor of 100 microfarads

• A resistor of 100k ohms

• A two- or three-position switch

The Circuit

The circuit, as shown below, should be constructed on the breadboard.

When the switch is in the position shown, the power supply is connected in series with the ammeter and a resistor to the capacitor. A voltmeter is connected across the capacitor. In this configuration, the capacitor will charge. The rate of charge is deliberately slowed by the resistor, which limits the current (by a great deal, having such a high value as 100,000 ohms). This slowing down of the charging process is important, as it allows you to read the voltage at various times in order to plot a graph of voltage against time.

When the switch is in the down position (as indicated on the diagram), the power supply is effectively disconnected from the circuit and the capacitor can now discharge through the ammeter and the resistor.

In both cases, the voltmeter will show the voltage across the capacitor. Note that the voltmeter will affect the circuit very slightly by having its own resistance (which is very high). Also note that the components in the circuit – i.e., the resistor and the capacitor – do not have precise values and there is always some inaccuracy in their values, although they are expected to be within certain tolerances. You can see the tolerances for a resistor quite easily on a resistor color chart that you can look up online. The final band (the lowest, as shown here) indicates the tolerance of the resistor. In the case described next, the band is colored silver.

This shows the bands on a resistor that identifies its value and tolerance.

Question

What are the possible maximum and minimum values for the resistor as given in this circuit, as indicated in the screenshot above?

The variables

The time is the independent variable, and the voltage and current are the dependent variables.

The Physics

The simplest form of a capacitor is two parallel conducting plates, as shown here.

This shows two rectangular parallel plates

When the capacitor is charged, one plate carries a positive charge, and the other plate carries an equal amount of negative charge.

The definition of capacitance is given by the amount of charge on one of the conductors divided by the potential difference between the plates. That is:

C = Q/dV

Voltage increases linearly with charge, so this quantity is a constant for a given capacitor and is known as the capacitance; it is a measure of the device’s ability to store charge.

The method

With the voltage set to 12V, switch on the power supply.

You need to get ready with a stopwatch at zero; use your wristwatch or your mobile phone, or even the clock from the task bar. With the power on, you now need to click on the switch to start the capacitor charging and start your stopwatch. Take a note of the voltage every 5 seconds for a full minute. After a minute, the capacitor will be fully charged. At this point, you can turn the power supply off.

To discharge the capacitor, click on the two-way switch; you will need to be ready with your stopwatch. Take readings every 5 seconds for a minute.

Note: If you stop charging before the capacitor is fully charged, the capacitor will hold its charge fairly well with just a small amount of leakage, and you can continue charging it at any subsequent time. You will notice that when the power supply is not on but the switch is in the charging position, the voltage across the capacitor will slowly drop. This is because the capacitor is slowly losing charge by leaking through the very high resistance of the voltmeter. There is no current indicated because the ammeter is not part of this circuit. Effectively when in this configuration, the circuit is as shown here:

This is a schematic of the circuit, showing the voltmeter connected in parallel to the capacitor.

Only the right-hand part of the circuit is complete, so the current flows. The left-hand part of the circuit is incomplete, so no current flows for the ammeter to detect.

The Video

Watch a video for the Capacitor Charge and Discharge e-practical here.

This shows how to use it and how to collect the data.

The E-Practical

Perform the experiment yourself, collect your own data, make mistakes and be able to correct them. The e-practical requires that your browser can run WebGL 2 (usually found on Windows browsers, safari on iOS, and various Mobile browsers, test with https://get.webgl.org/webgl2/). This link is for students and evaluation only, schools should purchase a site licence.

All the e-practicals will run on devices as small as a mobile 'phone. However, the best experience is on a PC using a mouse which gives very precise control, but if you are limited to a small device, consider using a stylus or a blue tooth mouse.

You can switch on the power supply by clicking the red on/off button. You should see the output indicator on the power supply screen indicate a connection, as shown here:

Closeup of the power supply showing its controls.

When the switch on the breadboard is forward, as shown here:

Closeup of the switch on the breadboard in the discharge position

The switch is in the discharge position; that is, the two contacts underneath the switch that are closer are connected. Think of the mechanism as that shown here:

Schematic of the two-way switch showing the internal connection.

The lever pivots on a hinge and slides a metal contact maker over two of the connecting prongs at a time. When the lever is to the left, the two right prongs are connected, and when it is to the right, the left two prongs are connected.

Try it yourself

The Results

Plot a graph of voltage on the Y-axis and time on the X-axis for the entire range of timings, both for charging and discharging.

These give the characteristic of an asymptotic curve. On charging, the charging rate slows as it approaches a maximum value. The charging rate is in fact an exponential function. For discharge, the function is:

V = V0e^-t/RC

Taking natural logs (logs to the base e) of both sides of this equation gives:

ln(V) = ln(V0e^-t/RC)

Multiplication within the brackets of the natural log function is equivalent to addition using the rule:

ln(AB) = ln(A) + ln(B)

This gives us:

ln(V) = ln(V0) + ln(e^-t/RC)

This simplifies to:

ln(V) = ln(V0) -t/RC

We can rearrange this to be the equation of a straight line:

ln(V) = -t/RC + ln(V0)

If you compare this with the standard form of the equation for a straight line:

y = mx + c

We can verify the discharge equation by plotting ln(V) on the Y-axis and t on the X-axis. The intercept will be ln(V0) and the gradient will be 1/RC. Fill in the following table with your results.

Plot ln(V) on the Y-axis against time on the X-axis. The gradient should be -1/RC. This should give a value for RC somewhere close to 10 (R = 100,000 Ohms, C = 10-4 Farads).

Further Discussion

Find out how to make a simple capacitor from foil and paper on the internet. Try making one and measuring its capacitance; does this conform to what the theoretical calculation of capacitance would give?

Theoretically, the capacitance is given by:

C = kAε0/d

Where A is the area, and d is the separation of the plates, ε0 is the permittivity of space (8.854 x 10|^-12 F/m) and k is the relative permittivity of the dielectric material between the places. In this case, this is paper and the value is around 3.8.

This section is adapted from material developed by Dr Robert Lucas and is related to the book High School and Undergraduate Physics Practicals, published by CRC Press.