Question

You are given 10 similar variable capacitors in which all the quantities the capacitance depends are changeable. Select all the possible ways of creating a capacitor with the capacitance of 4 times a single one:

a) replace the dielectric material with a material four times the dielectric constant

b) parallelly connect 4 of them without changing anything

c) decrease the distance between the plates 4 times of one capacitor and use this changed capacitor

d) increase the plate area of one capacitor 4 times and use this changed capacitor

e) increase the plate area 2 times and decrease the distance between plates 2 times of single capacitor and use this changed capacitor

Answer 1

a) As the capacitance of a capacitor is directly proportional to di electric constant, so if we replace a material with 4 times of di electric constant, its capacitance will be doubled.

b) when we connect capacitors parallely, capacitance are added, like if two same capacitors are added in parralel

their net capacitance becomes 2C. So, if we connect 4 of them parallely, their capacitance will be 4 times.

c) Capacitance is given by = where d is distance between plates, so if it is decreased to d/4, capacitance becomes 4 times, assuimng that it is a parallel plate capacitor.

d) Similarily increasing the plate area by 4 times will increase the capacitance by 4 times.

e) From the formula in part c, it is clear that if we increase the plate area by 2 times and decrease the distance between them by half, capacitance will become 4 times.