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Electrostatic Potential and Capacitance — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectrostatic Potential and Capacitance1 Mark
Question
For two statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, and R is also false.
Assertion (A): If the distance between parallel pates of a capacitor is halved and dielectric constant is made three times, then the capacitance becomes six times.
Reason (R): Capacitance of the capacitor does not depend upon the nature of the material of the plates.
✓

Answer

  1. A is true, but R is false.
Explanation:
The capacitance C, with dielectric between the plates, is given as
$\text{C}=\frac{\epsilon_0\text{KA}}{\text{d}}$
As, $\text{d'}=\frac{\text{d}}{2}\text{K'}=\text{3K},$ then new capacitance becomes
$\text{C'}=\frac{\epsilon_0\text{3KA}}{\frac{\text{d}}{2}}$
$\Rightarrow\text{C'}=\frac{6\epsilon\text{KA}}{\text{d}}=\text{6C}$
The capacitance C depends only on the geometrical configuration (shape, size, separation) of the system of two conductors.

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