An air capacitor has a capacitance12µF. When a dielectric is introduced between the plates, its capacitance becomes 18µF, the relative permittivity of the dielectric is:
Question
An air capacitor has a capacitance12µF. When a dielectric is introduced between the plates, its capacitance becomes 18µF, the relative permittivity of the dielectric is:
Solution
The relative permittivity (also known as the dielectric constant) of a material is given by the ratio of the capacitance of a capacitor filled with the dielectric to the capacitance of the same capacitor in a vacuum or air.
In this case, the capacitance of the air capacitor is 12µF and when the dielectric is introduced, the capacitance becomes 18µF.
So, the relative permittivity (εr) can be calculated using the formula:
εr = C/C0
where: C is the capacitance with the dielectric (18µF) and C0 is the capacitance without the dielectric (12µF).
Substituting the given values into the formula, we get:
εr = 18µF / 12µF = 1.5
So, the relative permittivity of the dielectric is 1.5.
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