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Capacitance is the measure of the electric charge that can be held by a conductor. It is defined as the ratio of the charge of the capacitor to the potential of the capacitor. The capacitance formula is expressed as C = Q / V. When the capacitors are connected in series, the capacitance formula is expressed by Cs = 1/C1 + 1/C2. Again, the capacitance formula is expressed by Cp = C1 + C2 if capacitors are connected in parallel. Where C1, C2, C3…….Cn is the capacitors and Capacitance is expressed in Farads. Let’s have a closer look at the topic and discuss some important questions.
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Key takeaways: Capacitance, capacitors, unit of capacitance, potential of a capacitor, electric charge, conductor, farad, electronic devices, electrostatic potential
Read More: Unit 1 Chapter 2 Electrostatic Potential and Capacitance
What is Capacitance?
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Capacitance is usually measured in a device with parallel plates by measuring the electric field between the two plates. It is the ability of an object to store charge. As the electric field between the plates increases, the charge that can be stored between them also increases. It depends on the shape, size, and distance between the conductors along with the type of medium between them. Any object that has the ability to store charges within itself has capacitance and is called a capacitor. Capacitors are found in almost all electronic devices to serve the simple task of storing charges. They are available in all shapes and sizes, according to the amount of charge they are required to store in themselves.
Capacitance
In a camera, the flash requires quite a lot of energy in a short period of time so that it can produce a flash with the needed brightness. The power needed to produce this brightness cannot be provided by a battery. Instead, an arrangement of capacitors is used to store enough energy and release it across the filament rapidly. Similarly, during a power failure, computers are bound to lose any critical data or files in the absence of a capacitor. The array of capacitors found in a computer charge automatically as soon as the power is on. In the situation of an emergency power failure, the capacitors lose charge through the circuit, thereby providing enough time for the computer to save critical files and data.
The video below explains this:
Capacitance Detailed Video Explanation:
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Formula of Capacitance
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The following is the basic formula of capacitance:
| C = QV |
Where,
C = the capacitance that is measured in farads,
Q = the charge that is measured in coulombs,
V = the voltage that is measured in volts.
Besides this, another formula can also be applied to calculate capacitance which is as follows:
| C = kε0Ad |
Where,
C = for capacitance,
K = for relative permittivity,
ε0 = for the permittivity of free space,
A = for the surface area of the plates and
d = for the distance between the plates.
If two capacitors are connected in a series connection, the formula becomes as follows:
| Cs = 1C1 + 1C2 |
Where,
C1 and C2 = to the respective capacitances of the capacitors and
Cs = to the capacitance in series.
Similarly, if two capacitors are connected in a parallel connection, the formula to find the capacitance of the overall arrangement is as follows:
| Cp = C1 + C2 |
Where Cp is the capacitance in parallel.
Unit of Capacitance
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The unit of capacitance is coulomb/volt which is called farad. Farad (F) is a large unit generally and in usual situations, the unit of microfarad (mF) is used.
Potential of a Capacitor
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In a parallel-plate capacitor, the potential difference between the two plates is the potential of the capacitor. A capacitor is generally the arrangement of two metallic plates separated by an insulating medium. Here, the positive charge on one plate, i.e., the positive plate, is equal to the negative charge on the other plate, i.e., the negative plate. This implies that the net charge on the capacitor will be equal to zero, as both the plates contain equal and opposite charges.
Capacitance and charge on capacitors plates
When a capacitor is supplied with an external charge via a battery or any other source, the two plates get accumulated with the charge. Consequently, when this capacitor gets connected to a circuit, the electric current starts flowing. The negative charge flows towards the positive charge, and this is how the charge on the capacitor gets neutralized.
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Things to Remember
- Capacitance is the ability of an object to store charge. It is the ratio of the charge of the conductor to the potential of the conductor.
- A capacitor is the device used to store charge.
- The capacitance of a capacitor is directly proportional to the charge on it and inversely proportional to the potential of it.
- C = QV, where Q is the charge and V is the potential of the capacitor.
- C = kε0Ad, where k is the relative permittivity, ε0 is the permittivity of free space, A is the surface area of the plates and d is the distance between the plates.
- Cs = 1C1 + 1C2 + 1C3 + . . . + 1Cn
- Cp = C1 + C2 + C3 + . . . + Cn
- Capacitance is measured in farads (F).
- The potential difference between the two plates of a capacitor is the potential of the capacitor.
Sample Questions
Ques: Find the capacitance of a capacitor where a charge of 10 C flows and where a potential of 4 V is given. (2 marks)
Ans: Charge (Q) = 10 C
Potential (V) = 4 V
C = QV
C = 104
= 2.5 F
Ques: A person entered a large cage made of metal, supported by pillars that were insulated. The cage was then charged using a powerful electric machine. Even though the person was afraid of getting a shock, they were safe inside the cage. What do you think is the reason behind this phenomenon? (2 marks)
Ans: As the cage is insulated, the charge supplied to it flows only through the outer surface of the cage. Moreover, the potential at every point remains the same which implies that there is no potential difference between any two points in the cage. Therefore, the person remained safe inside the cage.
Ques: What is the capacitance of a parallel-plate capacitor that holds a charge of 100 μC and has a potential difference of 20 mV? (2 marks)
Ans: Q = 100 μC
V = 20 Mv
C = QV
= 100 x 10-620 x 10-3
C = 0.005 F
= 5 mF
Ques: Consider a parallel-plate capacitor charged with a battery having constant voltage. The battery is removed from the circuit when the capacitor reaches its maximum charge. Find out the changes that can occur on the following if the parallel plates are pushed closer to each other. (3 marks)
Ans: Following are the changes:
- Charge: The charge deposited on the plates is not affected on removing the battery. Therefore, the charge and the charge density remain the same when the plates are pushed closer together.
- Capacitance: As C is inversely proportional to d, if the distance between the plates is decreased, the capacitance increases.
- Voltage: As C is inversely proportional to V, when capacitance increases, the voltage decreases.
Ques: Calculate the effective capacitance between a and b from the figure given below: C1 = C3 = 100 μF, C2 = C4 = 200 μF. (2 marks)
Ans: Resultant of C1 and C2 = C1 + C2 = 300 μF
Resultant of C3 and C4 = C3 + C4 = 300 μF
Effective capacitance = 1300 + 1300
C = 150 μF.
Ques: Calculate the capacitance in a circuit where capacitors 11 F and 2 F are connected: (4 marks)
(a) In series
(b) In parallel
Ans: C1 = 11 F
C2 = 2 F
- Cs = 1C1 + 1C2
= 111 + 12
= 2 + 1111 x 2
= 1322
Cs = 0.59 F
- CP = C1 + C2
= 11 + 2
CP = 13 F
Ques: Consider a capacitor with 0.1 m2 surface area, whose plates are 0.01 m away from each other. What is the charge that these plates can store when it is connected to an 8 V battery if there is air between the plates? (4 marks)
Ans: A = 0.1 m2
D = 0.01 m
V = 8 V
K = 1 (since there is air between the plates)
ε0 = 8.854 x 10-12
C = kε0Ad
= 1 x 8.854 x 10-12 x 0.10.01
= 8.854 x 10-11 F
Q = C x V
= 8.854 x 10-11 x 8
Q = 70.8 x 10-11 C
Ques: If the distance between the plates of a capacitor is 2 x 10-3 m, find out the surface area of the plates. The capacitance of the capacitor is 1 F. (4 marks)
Ans: d = 2 x 10-3 m
C = 1 F
C = kε0Ad
K = 1
ε0 = 8.85 x 10-12
A = dCkε0
= 2 x 10-3 x 11 x 8.85 x 10-12
A = 2.3 x 108 m2
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