A parallel plate condenser with oil between the plates( dielectric const. of oil K=2) has a capacitance C . if the oil is removed then what will be the capacitance of the capacitor?
C =ε(o) •ε•A/d
C1= ε(o) •A/d
C1 =C/ε = C/2
Whats ans
To calculate the capacitance of a parallel plate capacitor with a dielectric material, we can use the formula:
C = (ε * A) / d
Where:
C is the capacitance
ε is the permittivity of the dielectric material
A is the area of the capacitor plates
d is the distance between the plates
In the given scenario, the dielectric constant of oil is K = 2. The permittivity of the dielectric material is related to the dielectric constant by the equation:
ε = ε₀ * K
Where:
ε₀ is the permittivity of free space
Assuming the capacitance with the oil between the plates is C, we can rewrite the formula as:
C = (ε₀ * K * A) / d
Now, if the oil is removed, the dielectric constant becomes 1 (for air), and the formula for the new capacitance, C', is:
C' = (ε₀ * K' * A) / d
where K' is the new dielectric constant (for air, K' = 1).
From the above formulas, we can see that the capacitance of the capacitor is inversely proportional to the dielectric constant. Therefore, when the oil (K = 2) is replaced with air (K' = 1), the capacitance will double.
Hence, the capacitance without the oil will be 2C.