Unit 2: Science for Engineering
LO3: Understand fundamental scientific principles of
electrical and electronic engineering
Electric fields, field strength and capacitance – the
RC circuit and time constant
Task 1
Charging a capacitor in series with a resistor
The circuit below shows a series RC circuit. When charging, capacitor voltage is described by the
equation:
Vc = Vo(1 - e- t/RC)
where the potential difference (p.d.) at time t is Vc and at t = 0, the p.d. is Vo. In the circuit Vo is 9 V.
Your task is to perform an experiment to explore the charging of a capacitor.
Connect the power supply, resistor and capacitor as shown in the circuit diagram. Do not switch on the
power supply yet – your teacher will need to check the circuit first!
You will need a voltmeter (or multimeter) to measure the voltage across the capacitor, and a stopwatch
to do this at 10 second intervals
d.c. Voltage
Source
9V
+
470 kΩ
100 µF
February 2015
Vc
Switch on the power supply and record voltage readings every 10 seconds up until 300 seconds (5
minutes). Tabulate your results in a table as shown below – including both calculated and measured
voltage.
Time (seconds)
0
Voltage across capacitor
Voltage across capacitor
(volts)
(volts)
Calculated
Measured
0
0
10
20
30
.
.
300
Once you have completed the table, plot your results using either graph paper or Microsoft Excel – a
simple x-y graph of time (x-axis) and voltage (y-axis) with the points joined up will do. Remember to start
a time=0 seconds with 0 volts across the capacitor!
Questions:
1. What do you notice about the shape of the graph?
2. What is the time constant for the circuit (given by RC)?
February 2015
3. How does the time for the capacitor to fully charge (to approximately 9 V) relate to the time
constant RC?
4. Comment on any errors between calculated and measured values. What do you think causes
errors?
Task 2
Effects of varying the value of C in the circuit
You are going to repeat the experiment from Task 1 using a higher-value capacitor.
d.c. Voltage
Source
9V
+
470 kΩ
150 µF
February 2015
Vc
Once your circuit has been checked by your teacher, switch on the power supply and record voltage
readings every 10 seconds up until 300 seconds (5 minutes). Tabulate your results as last time in a
table as shown below.
Time (seconds)
0
Voltage across capacitor
Voltage across capacitor
(volts)
(volts)
Calculated
Measured
0
0
10
20
30
.
.
300
Plot your results as before.
February 2015
Questions:
1. What do you notice about the shape of the graph this time – how has it changed from that plotted
in Task 1?
2. What has been the effect on the circuit time constant by making the value of C bigger?
3. Does the capacitor charge fully (to approximately 9 V) in 300 seconds – and if not how long will it
take?
4. If the value of the capacitor cannot be changed, what is another way of changing the circuit time
constant?
February 2015
Task 3
Discharging a capacitor in series with a resistor
When discharging, capacitor voltage is described by the equation:
Vc = Vo e- t/RC
where the potential difference at time t is Vc and at t = 0, the p.d. is Vo. In the circuit Vo is taken as 9 V
when the capacitor is fully charged.
Connect the circuit as shown below. For this task you are going to plot the voltage across the capacitor
when it is discharging.
d.c. Voltage
Source
9V
+
switch
1
470 kΩ
Vc
2
470 kΩ
100 µF
Have your circuit checked by your teacher.
With the switch at position 1, the capacitor will charge up (to nearly the supply voltage). Begin by
charging the capacitor fully. Remember, it will take approx. 300 seconds to charge fully. You will be
able to see this on the voltmeter.
Once the capacitor is fully charged move the switch to position 2. The capacitor will now discharge
through the 470 k resistor. Start recording voltage across the capacitor as soon as the switch is moved
to position 2.
February 2015
Tabulate your results as last time in a table as shown below. Remember to include both calculated and
measured voltage.
Time (seconds)
0
Voltage across capacitor
Voltage across capacitor
(volts)
(volts)
Calculated
Measured
0
0
10
20
30
.
.
300
Plot your results as before.
Questions:
1. What do you notice about the shape of this graph for discharging?
2. What is the time constant for the circuit (given by RC)?
February 2015
3. How does the time for the capacitor to fully discharge relate to the time constant RC?
February 2015