Question

In a parallel capacitor, the capacitance:
$\left( {\text{A}} \right)$ Increases with increase in the distance between the plates
$\left( {\text{B}} \right)$ Decreases if a dielectric material is put between the plates
$\left( {\text{C}} \right)$ Increases with decrease in the distance between the plates
$\left( {\text{D}} \right)$ Increases with decrease in the area of the plates

Answer 1

Hint: The direction of the electric field is toward the direction in which the positive test charge would flow. Capacitance is defined as the limitation of the body to store the electric charge. Every capacitor has capacitance. The parallel-plate of the capacitor consists of two metallic plates of area A, and it is separated by the distance d.

Formula Used:
The parallel plate of the capacitor formula is given by ${\text{C = }}\dfrac{{{\text{k}}\varepsilon {\rm A}}}{{\text{d}}}$,
Here \[{\text{C = }}\] capacitance of the capacitors, \[{\varepsilon _0} = \] permittivity of space \[\left( {8.854\; \times \;10 - 12\;F{\text{ per }}meter} \right)\], \[k = \] relative permittivity of dielectric material, \[d = \] separation between the plates, A= area of plates.

Complete step by step answer:
Explaining the given options:
$\left( {\text{A}} \right)$ The given option says that the distance between the plates of the capacitor increases the capacitance but according to the formula, the distance between plates is inversely proportional to the capacitance of the capacitor.
$\left( {\text{B}} \right)$ The given option says that if we insert any dielectric between the plates of the capacitor, it can fully occupy the whole region between the plates or it may be partially occupied. When a dielectric is placed between the two plates of the parallel plate capacitor, it is polarized by the electric field present. Inserting a dielectric material increases the capacitance of the capacitor by a factor of dielectric constant.
$\left( {\text{C}} \right)$ The given option explains correctly according to the formula which defines the relation between the distance between the plates and capacitances of the capacitor which is inversely proportional to each other.
$\left( {\text{D}} \right)$ This option says the relationship between the area and the capacitance of the capacitor which is not true, the area and the capacitance of the capacitor are directly proportional to each other.

Hence the correct option is $\left( {\text{C}} \right)$

Note: When a dielectric material is placed between the plates of the parallel plate capacitor then due to polarization of charges on either side of the dielectric. It may produce an electric field of its own sources and which acts in a direction opposite to the field due to its own source.