Embibe Experts Solutions for Chapter: Capacitance, Exercise 2: Exercise-2

Assertion: If the potential difference across a plane parallel plate capacitor is doubled then the potential energy of the capacitor becomes four times under all conditions.

Reason: The potential energy $U$ stored in the capacitor is $U=\frac{1}{2}V{C}^2,$ where $C$ and $V$ have usual meanings.

Assertion : A charged plane parallel plate capacitor has half interplanar region (l) filled with dielectric slab. The other half region II has air, Then the magnitude of net electric field in region $I$ is less than that in region Il.

Reason : In a dielectric medium induced (or polarised) charges tend to increase the electric field inside the dielectric.

Assertion : A parallel plate capacitor is charged to a potential difference of $100 \mathrm{V},$ and disconnected from the voltage source. A slab of dielectric is then slowly inserted between the plates. Compared to the energy before the slab was inserted, the energy stored in the capacitor with the dielectric is decreased.

Reason : When we insert a dielectric between the plates of a capacitor, the induced charges tend to draw the dielectric into the field ( just as neutral objects are attracted by charged objects due to induction). We resist this force while slowly inserting the dielectric, and thus do negative work on the system, removing electrostatic energy from the system.

Assertion : The circuits containing capacitor be handled cautiously even when there is no current.

Reason : A charged capacitor, can discharge through our body and harm us.

Assertion : Increasing the charge on the plates of a capacitor means increasing the capacitance.

Reason : Because $Q=CV\Rightarrow Q\propto C.$

Assertion : If three capacitors of capacitance $C_1<C_2<C_3$ are connected in parallel then their equivalent capacitance $C_p>C_s$

Reason : $\frac{1}{C_p}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

Assertion: The capacitance of a capacitor remains the same even if the charge is varied on it.

Reason: Capacitance depends upon nearly medium as well as size and shape of capacitor.

Assertion : The force with which one plate of a parallel plate capacitor is attracted towards the other plate is equal to square of surface density per $\epsilon$ per unit area

Reason : The electric field due to one charged plate of the capacitor at the location of the other is equal to surface density per $\epsilon$