1
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

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

A
1.5
B
2.5
C
1.2
D
3
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

A source of potential difference $$V$$ is connected to the combination of two identical capacitors as shown in the figure. When key '$$K$$' is closed, the total energy stored across the combination is $$E_{1}$$. Now key '$$K$$' 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 $$E_{2}$$. The ratio $$E_{1} / E_{2}$$ will be :

A
$$\frac{1}{10}$$
B
$$\frac{2}{5}$$
C
$$\frac{5}{13}$$
D
$$\frac{5}{26}$$
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

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

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

A
$$200 \,\mu \mathrm{C}$$
B
200 C
C
$$10 \,\mu \mathrm{C}$$
D
10 C
4
JEE Main 2022 (Online) 25th July Evening Shift
+4
-1

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 $$\left( {{{{R_2}} \over {{R_1}}}} \right)$$ is :

A
$${n \over {n - 1}}$$
B
$${{2n} \over {2n + 1}}$$
C
$${{n + 1} \over n}$$
D
$${{2n + 1} \over n}$$
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