Page 11 - PRE-U STPM PHYSICS TERM 2

Physics Term 2 STPM Chapter 13 Capacitors

Example 3

A capacitor made from two thin, flat metal sheets
separated by an insulating material has a capacitance C.
Each metal sheet is then cut into four identical sheets,
which are used to make the capacitor as shown. The
13 separation between the interleaved sheets is filled with 13

the same insulating material.
Find in terms of C, the capacitance of the reconstructed
capacitor.
Solution:
Exam Tips
If A = area of each large metal sheet
d = separation between sheets To determine the number of capacitors in the
question: Count the number of spaces between
ε ε A two plates
r 0
then C = ——–
d
The reconstructed capacitor consists of 7 capacitors connected in parallel. Four plates are to one
terminal, and another four to the other terminal.
A C
,
Each capacitor is of area — hence of capacitance = —
4 4
C
Hence capacitance of 7 capacitors each of capacitance — in parallel
4
C ’ = 7 × ( —) 7
C
= —C
4 4
Example 4

A parallel-plate capacitor consisting of two metal plates
separated by a distance x has capacitance C. Each metal plate x x x
is cut into three identical small plates and connected to form Metal
the system of capacitors shown in the diagram. The separation plate
between plates remains as x.
Deduce in terms of C, the effective capacitance of the arrangement
shown in the diagram.

Solution: +Q + – –Q
+ –
+ –
– + –
–Q –Q –Q
–Q – + + – – + + – + – + – +4Q –4Q
1 2 3 4 + 5 – +Q + – –Q + –
– + + – – + + – + + – – + – + –
+ – + – + –
– + + – – + + – + + – – + + – –
+ – + + – –
– + + – – + + – + – + – + –
+4Q –4Q +Q + – –Q + –
+Q +Q +Q +Q + + + – –
Figure (a)
When the arrangement is connected to a voltage supply, the +Q + + – – –Q
charges on the plates are as shown in Figure (a). + –
Since the number of spaces between plates is 5, there are 5 + –
capacitors. Figure (b)

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