Solved Examples of Capacitance Formula
Example 1: A spherical capacitor has an inner sphere of radius 12 cm and an outer sphere of radius 13 cm. The outer sphere is Earthed and the inner sphere is given a charge of 2.5 µC. Find the capacitance of the capacitor.
Solution:
Given,
- Radius of Inner Sphere, (r2) = 12 cm = 0.12 m
- Radius of Outer Sphere, (r1) = 13 cm = 0.13 m
- Charge on Inner Sphere (q) = 2.5 μC = 2.5 x 10-6 C
Capacitance of Spherical Capacitor is,
Permittivity of free space is 8.85 x 10-12 C2 N-1 m-2.
Substituting the values in the above expression,
C = 2.08×10-11 F
The required capacitance of the capacitor is 2.08×10-11 F
Example 2: A capacitor is completely charged with 650 nC by a voltage source that has 275 V. The initial air gap of the capacitor was 7 mm. What is the stored energy if the air gap is now 3 mm?
Solution:
Given,
- Charge on Capacitor (Q) = 650 nC = 650 × 10-9 V
- Voltage of Source (V) = 275 V
- Initial Air Gap (d1) = 7 mm
- Final Air Gap (d2) = 3 mm
Using Capacitance Formula
C = Q / V
C = (650 × 10-9) / 275
C1 = 2.36 × 10−9 F
Gap between the plates changed from 7 mm to 3 mm
C1d1 = C2d2
C2 = C1d1/d1
C2 = [(2.36 × 10−9) (7 × 10−3)] / (3 × 10−3)
= 5.5 × 10−9 F
Energy stored in the Capacitor is given by the formula,
E = (1/2) C2V2
Substituting the values in the above expression,
E = 5.5×10−9× (275)2
= 207.9 μ J
Thus, the enegry stored in the capacitor is 207.9 μ J
Capacitance
Capacitance is defined as the capacity of any material to store electric charge. The substance that stores the electric charge is called a capacitor, i.e. the ability of the capacitor to hold the electric charge is called capacitance. It is denoted with the symbol C and is defined as the ratio of the electric charge stored inside a capacitor by the voltage applied.
Thus, any material that has a tendency to store electric charge is called a capacitor and the ability of the material to hold electric charge is called the capacitance of the material. In this article, we will learn about capacitance, its formula, capacitor, and others in detail.
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