CBSE Class 12 Physics 2016 Delhi Set 1 Paper

Question : 15 of 26

Marks: +1, -0

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

\bo {Y}

contains a dielectric medium of

ε_{ {\r}}=4

(i) Calculate capacitance of each capacitor if equivalent capacitance of the combination is

4 µ {\F}

.
(ii) Calculate the potential difference between the plates of

X

and

Y

.
(iii) Estimate the ratio of electrostatic energy stored in

X

and

Y

Solution:

(i) Calculation of capacitance of each capacitor
(ii) Calculation of potential difference
(iii) Estimation of ratio of electrostatic energy
(i) Let

C_X=C

C_γ=4 C

(as it has a dielectric medium of

ε_γ

=4

)
For series combination of two capacitors

\;{1}/{C}\;=\;{1}/{C_X}+\;{1}/{C_Y}

⇒ \;\; \;{1}/{4 µ F}\;=\;{1}/{C}+\;{1}/{4 C}

\;{1}/{4 µ F}\;=\;{5}/{4 C}

⇒ \;\; C\;=5 µ F

\;\text " Hence "\; \;\; C_X\;=5 µ {\F}

C_Y\;=20 µ {\F}

Hence

C_X=5 µ {\F}

C_γ=20 µ {\F}

\;\;\text " (ii) Total charge "\; Q=C V

\;=4 µ {\F} × 15 {\V}=60 µ {\C}

\;V_X=\;{Q}/{C_X}=\;{60 µ {\C}}/{5 µ {\F}}=12 {\V}

\;V_Y=\;{Q}/{C_Y}=\;{60 µ {\C}}/{20 µ {\F}}=3 {\V}

\;\;\text " (iii) "\; \;{E_x}/{E_y}=\;{\;{Q^2}/{2 C_X}}/{{Q^2}/{2 C_Y}}

=\;{C_Y}/{C_X}=\;{20}/{5}=4: 1

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