JEE Main Capacitor Practice Questions With Solutions

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R.

Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason R : Capacitance of metallic spheres depend on the radii of spheres

In light of the above statements, choose the correct answer from the options given below.

A parallel plate capacitor has plate area 40 cm${}^2$^{2} and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

Two identical thin metal plates has charge $q_1$q_{1} and $q_2$q_{2} respectively such that $q_1>q_2$q_{1} > q_{2}. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

A slab of dielectric constant $\mathrm{K}$K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}\mathrm{d}$\frac{3}{4} \textrm{ } d, where $\mathrm{d}$d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :

(Given ${\mathrm{C}}_0$C_{0} = capacitance of capacitor with air as medium between plates.)

Two capacitors, each having capacitance $40\mu \mathrm{F}$40 \mu F are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $\mathrm{K}$K such that the equivalence capacitance of the system became $24\mu \mathrm{F}$24 \mu F. The value of $\mathrm{K}$K will be :

A source of potential difference $V$V is connected to the combination of two identical capacitors as shown in the figure. When key '$K$K' is closed, the total energy stored across the combination is $E_1$E_{1}. Now key '$K$K' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now $E_2$E_{2}. The ratio $E_1/E_2$E_{1} / E_{2} will be :

The total charge on the system of capacitors $C_1=1\mu \mathrm{F},C_2=2\mu \mathrm{F},{\mathrm{C}}_3=4\mu \mathrm{F}$C_{1} = 1 \mu F , C_{2} = 2 \mu F , C_{3} = 4 \mu F and ${\mathrm{C}}_4=3\mu \mathrm{F}$C_{4} = 3 \mu F connected in parallel is :

(Assume a battery of $20\mathrm{V}$20 \textrm{ } V is connected to the combination)

Capacitance of an isolated conducting sphere of radius R₁ becomes n times when it is enclosed by a concentric conducting sphere of radius R₂ connected to earth. The ratio of their radii $\left(\frac{R_2}{R_1}\right)$\left(\right. \frac{R_{2}}{R_{1}} \left.\right) is :

A condenser of $2\mu \mathrm{F}$2 \mu F capacitance is charged steadily from 0 to $5\mathrm{C}$5 C. Which of the following graph represents correctly the variation of potential difference $(\mathrm{V})$\left(\right. V \left.\right) across it's plates with respect to the charge $(Q)$\left(\right. Q \left.\right) on the condenser?

C_o is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $\epsilon$\epsilon_r (as shown in Fig. 2), the new capacitance of the capacitor will be :