PHY1100 Physics Practical I
UNIVERSITY OF MALTA
MSIDA, MALTA
8 March 2012
CONTENTS
2
Contents
1 The
1.1
1.2
1.3
1.4
2 —
Time Constant for
Aim . . . . . . . . .
Apparatus . . . . . .
Description . . . . .
Procedure . . . . . .
Capacitor Circuits
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1
1.1
THE TIME CONSTANT FOR CAPACITOR CIRCUITS
The Time Constant for Capacitor Circuits
Aim
Determine the time constant for two capacitors in series and parallel.
1.2
Apparatus
9V DC Power Supply, Two 47 µF capacitors, Voltmeter, Lengths of
wires, 1 M Ω Resistor, Stopwatch
1.3
Description
Given two capacitors of capacitances C1 and C2 respectively, they can be
connected in either an parallel or series circuit configuration as shown in
Figs.(1.3,1.3). For two capacitors in series the effective (or equivalent)
is found by
1
1
1
=
+ ,
(1.3.1)
Cef f
C1 C2
while for two capacitors connected in parallel the effective capacitance
is determined through
Cef f = C1 + C2 .
(1.3.2)
The effective capacitance is in particular the capacitance that a capacitor would have if it were to replace the capacitors in the circuit. Thus
the characteristics of the effective capacitor will be equivalent to the behavior of the two capacitors in this circuit.
On the other hand for a capacitor with capacitance C connected in series
with a resistor R having a voltage V0 when charged to its maximum
potential difference, the discharging of the capacitor obeys the relation
V = V0 e−t/CR .
(1.3.3)
The point at which the potential difference is equal to 1/e of the capacity
value is called the time constant. By comparison with Eq.(1.3.3) this
value will theoretically be equal to T = CR.
1
4
THE TIME CONSTANT FOR CAPACITOR CIRCUITS
Figure 1: CR Circuit with two capacitors connected in parallel
Figure 2: CR Circuit with two capacitors connected in series
1.4
Procedure
1. Connect the two capacitors in parallel as shown in Fig.(1.3) and use
voltmeter to measure the potential difference across the capacitors.
2. Charge the capacitors by closing the switch S2 while keeping S1 open.
3. Open S2 after some time when the capacitors have reached their
maximum charge.
4. At the same time close S1 and start the stopwatch. Taking suitable
5
1
THE TIME CONSTANT FOR CAPACITOR CIRCUITS
time intervals take note of the potential difference across the capacitors.
5. Plot a graph of potential difference against time and find the time
constant from this graph.
6. By plotting a suitable straight line graph determine the time constant
of the circuit and compare this with the theoretical value T = Cef f R.
Also compare time constant from the first graph with that obtained from
the second.
7. Repeat the above procedure for the two capacitors connected in series
as shown in Fig.(1.3) remembering to change the theoretical value of the
capacitance due to the new configuration of the circuit.
2
6
2
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