| Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as: |
| Assertion (A): If distance between the parallel plates of a capacitor is halved, then its capacitance is doubled. |
| Reason (R): The capacitance depends on the introduced dielectric. |
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
C) Assertion (A) is true but Reason (R) is false
D) Assertion (A) is false and Reason (R) is also false
Correct Answer: B
Solution :
(b) The capacitance of a parallel plates capacitor is given by \[C=\frac{{{\varepsilon }_{0}}A}{d}\]where A is area of each plate, d is the distance between plates. \[\therefore \,\,\,\,\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{\frac{{{\varepsilon }_{0}}A}{d}}{\frac{{{\varepsilon }_{0}}A}{d/2}}=\frac{1}{2}\] \[\therefore \,\,\,{{C}_{2}}=2{{C}_{1}}\] When dielectric of dielectric constant K is introduced in between the plates, then the capacitance \[C=\frac{K{{\varepsilon }_{0}}A}{d}\]i.e., \[C\propto K\]Capacitance C depends on introduced dielectric.
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