-->

Electrostatic Potential And Capacitance

Question
CBSEENPH12039296

Two parallel-plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates, while Y contains a dielectric medium of straight epsilon subscript straight r space end subscript equals space 4



i) Calculate capacitance of each capacitor if the equivalent capacitance of the combination is 4 μF
ii) Calculate the potential difference between the plates x and Y

iii) Estimate the ratio of electrostatic energies stored in x and Y

Solution

i) 
Capacitance of a parallel plate capacitor is given by, 

straight C space equals space fraction numerator straight epsilon subscript straight o space straight epsilon subscript straight r space straight A over denominator straight d end fraction

Capacitance space of space plate space straight Y space is comma space

straight C subscript straight Y space equals space fraction numerator straight epsilon subscript straight o 4 straight A over denominator straight d end fraction

Capacitance space of space plate space straight X space is comma space

straight C subscript straight X space equals space fraction numerator straight epsilon subscript straight o straight A over denominator straight d end fraction

Thus comma space

space space space space space space straight C subscript straight Y space equals space 4 space straight C subscript straight X
rightwards double arrow space straight C subscript eq space equals space fraction numerator straight C subscript straight X space straight C subscript straight Y over denominator straight C subscript straight X space plus straight C subscript straight Y space end fraction space equals space 4 space μF

rightwards double arrow space fraction numerator straight C subscript straight X space left parenthesis 4 straight C subscript straight X right parenthesis over denominator 5 space straight C subscript straight X end fraction space equals space 4 space straight mu space straight F

rightwards double arrow space space straight C subscript straight X space equals space 5 space straight mu space straight F

rightwards double arrow space space straight C subscript straight Y space equals space 20 space μF 
ii) 
Potential difference between plates X and Y can be calculated as, 
            Q = CV 
rightwards double arrow space straight C subscript straight X space straight V subscript straight X space equals space straight C subscript straight Y straight V subscript straight Y space space

rightwards double arrow space straight V subscript straight X over straight V subscript straight Y space equals space straight C subscript straight Y over straight C subscript straight X space equals space 4

rightwards double arrow space straight V subscript straight X space equals space 4 space straight V subscript straight Y space

Also comma space straight V subscript straight Y space plus space straight V subscript straight X space equals space 15 space

rightwards double arrow space straight V subscript straight Y space equals space 3 space straight V space

rightwards double arrow space straight V subscript straight X space equals space 12 space straight V 
iii) 
The ratio of electrostatic energies can be calculated as: 

straight E space equals space fraction numerator straight Q squared over denominator 2 straight C end fraction

rightwards double arrow space straight E subscript straight X over straight E subscript straight Y space equals space straight C subscript straight Y over straight C subscript straight X space equals space 4 space

rightwards double arrow space straight E subscript straight x over straight E subscript straight Y space equals space 4 over 1

Some More Questions From Electrostatic Potential and Capacitance Chapter