A paper or plastic capacitors has metal foil  
strip as their conductor plates.  
plate thereby providing a thin insulating  
layer between the plates. The thinner the  
layer, the higher the capacitance.  
Note that: Electrolytic capacitors are  
connected with great care. Their ends are  
labelled positive or negative as safety  
precautions because a wrong connection can  
lead to an explosion.  
The insulating materials are rolled up and  
sealed inside a metal box so as to prevent  
moisture from entering.  
Air filled capacitor  
This is the capacitor in which the insulating  
(dielectric) material is air.  
Mica capacitor  
The capacitance of such capacitor is altered  
by changing the overlapping area between  
the plates.  
This is the capacitor in which the sheets of  
metal foil are separated by strips of mica as  
dielectric material.  
Note that, air filled capacitor is an example  
of variable capacitor which are mainly used  
for tuning radios.  
Variable capacitor is the one whose  
capacitance can be varied. Fixed capacitor is  
the one whose capacitance cannot be  
changed  
Mica is preferred because it is a natural  
mineral and splits easily into very thin  
sheets.  
CHARGING A CAPACITOR  
Charging a capacitor is the process of  
increasing the potential difference across a  
capacitor’s plates by connecting it to a  
power supply with a higher voltage.  
Electrolytic capacitor  
This is the capacitor in which the metal  
sheets are separated by a paper soaked in a  
chemical compound. The soaked paper is  
not an insulating material.  
A capacitor is charged by connecting its  
plates with the terminals of a cell. In this  
way the current flows in the plates.  
Action  
As the capacitor charges, a thin layer of  
aluminium oxide are formed on the positive  
Due to the presence of insulation between  
the plates of the capacitor, electrons tend to  
accumulate on the plate connected to the  
negative terminal of the cell.  
There could be enough heat to melt the wire  
or even cause sparks or explosion.  
DISCHARGING A CAPACITOR  
The current flows until the potential  
difference across the capacitor is equal to  
the voltage of the charging cells. Charging  
on the capacitor then stops.  
Capacitor discharge is the process of  
releasing the electrical charge stored in a  
capacitor.  
A capacitor can be discharged by connecting  
its plates together through a resistor as  
shown below.  
The figure below shows the graph of charge  
against time during charging the capacitor.  
Action  
When the two plates of a capacitor are  
connected by a conducting wire, a current  
flows between the plates and the conducting  
wire. This causes the electrons to flow from  
the conductive plates of the capacitor to the  
circuit, which then causes the capacitor to  
discharge.  
From the graph, the charge increases  
exponentially to maximum value.  
The slope of the graph represents the current  
and the area under the graph of current  
against time represents the charge.  
Example 01  
The voltage between the plates of the  
capacitor decreases until it reaches zero.  
When the potential difference between the  
plates is zero, the electrons stop to flow and  
the capacitor is neutral.  
State the function of the resistor during  
charging process of the capacitor  
Answer  
The resistor prevents current the high  
current in the capacitor plates which may  
cause heating or explosion  
The graph of charge against time during  
discharging of a capacitor is shown below.  
Example 02  
What happen if you don’t use a resistor with  
a capacitor during charging or use of small  
resistance?  
Answer  
To adjust voltage rating and consequently  
capacitance, capacitors are connected either  
in series or in parallel.  
Capacitors in series  
One capacitor of a certain value can be  
replaced by a number of capacitors joined  
together in series to give the same effective  
capacitance as shown below.  
Note  
The rate at which the capacitor charges and  
discharges is called time constant.  
Time constant is the product of resistance  
and capacitance of the capacitor.  
Time constant=resistance ×capacitance  
Points to note  
A capacitor with small time constant charges  
and discharges faster  
When capacitors are in series, the charges in  
the plates are the same (have equal charge)  
but different potential difference develops  
between the plates.  
Construction of air filled capacitor  
If the capacitors are arranged in series, the  
value of the total capacitance is very small  
(less than the value of the smallest  
capacitance).  
This is done by arranging any two parallel  
conductors such as metal plates placed close  
together but a suitable fixed distance with  
the air as an insulating medium (dielectric)  
between the plates of the capacitor.  
The effective capacitance in series is given  
by:  
1
1
1
1
=
+
+
CT  
C1  
C2 C3  
How to derive the formula  
Step 1: To find the total potential difference,  
V.  
COMBINATION OF CAPACITORS  
V= V1+ V2+V3  
Capacitors have voltage rate that should not  
be exceeded. Continuous charging by using  
large voltage can result in an explosion as  
the potential difference between the plates  
can break the insulation.  
Step 2: To find the p.d on each plate by  
using the same (equal amount of) charge.  
Q
Q
Q
Q
10μF, 20μF and 30μF, respectively.  
Calculate the value of a single capacitor that  
could replace them.  
V=  
,V1=  
, V2=  
and V3=  
C
T
C
1
C
2
C
3
Solution  
1
1
1
1
Step 3: To substitute the value above in step  
one  
=
=
=
=
+
+
+
CT  
C1  
C2 C3  
1
1
1
1
Q
Q
Q
Q
+
=
+
+
CT  
10  
20 30  
CT  
C1 C2  
C3  
1
6+3+2  
60  
CT  
Step 4: Fact out Q on either side  
1
11  
60  
1
1
1
1
CT  
Q [  
] = Q ⌈  
+
+
CT  
C1 C2  
C3  
60  
CT= ⌈ ⌉ μF  
Step 5: If we divide by “Q” both sides, we  
get.  
11  
CT= 5.45μF  
1
1
1
1
=
+
+
The value of a single capacitor that could  
replace them is 5.45μF capacitor.  
CT  
C1  
C2 C3  
Special case: when there are only two  
capacitors in series  
Example 02  
Two capacitors X and Y are arranged as  
shown on the figure below.  
The effective capacitance can be obtained by  
using the formula below:  
Use the information on the diagram to  
determine the amount of charge in each  
plate of the capacitors.  
1
1
1
=
+
CT  
C1  
C2  
By finding the LCM and make the”CT  
“subject we get  
Solution  
The two capacitors are arranged in series,  
hence:  
C1C2  
CT=  
C1+C2  
Step I: To find the effective (total)  
capacitance of the system.  
Example 01  
Three capacitors A, B and C, are arranged in  
series. Their capacitances are given as