CBSE Class 12 · 2016 · Delhi · CapacitanceShort Answer

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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

ε_{r} = 4

. (i) Calculate the capacitance of each capacitor if the equivalent capacitance of the combination (in series) 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) The dielectric makes

Y = ε_{r} X = 4 X

.
In series:

\frac{1}{4} = \frac{1}{X} + \frac{1}{4 X} = \frac{5}{4 X}

X = 5 μ F, Y = 20 μ F

(ii) Series charge for a 15 V supply:

q = C_{e q} V = 4 \times 15 = 60 μ C

V_{X} = \frac{q}{X} = \frac{60}{5} = 12 V, V_{Y} = \frac{q}{Y} = \frac{60}{20} = 3 V

(iii) With the same charge,

U = \frac{q ^{2}}{2 C}

, so:

\frac{U _{X}}{U _{Y}} = \frac{C _{Y}}{C _{X}} = \frac{20}{5}

\frac{U _{X}}{U _{Y}} = 4

CBSE Class 12 Board · 2016 · Delhi · Subjective

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CBSE Class 12 · 2016 · Delhi · CapacitanceShort Answer

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