Question 162: Electrostats & Capacitance

Question

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.

Accepted Answer

The amount of charge on each sphere will be the same if they are charged to the same potential. Whether the sphere is solid or hollow doesn't affect the amount of charge stored on the sphere as long as they have the same radii and are charged to the same potential.
Therefore, assertion A is false
As we know, capacitance of spherical conductor
$$
\mathrm{C}=4 \pi \varepsilon_0 \mathrm{R}
$$
So, capacitance does not depend on its charge, it depends only on the radius of the conductor (R).
Therefore, Reason $\mathrm{R}$ is true.

Answer

Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are true but $$\mathbf{R}$$ is not the correct explanation of $$\mathbf{A}$$

Answer

Both $$\mathbf{A}$$ and $$\mathbf{R}$$ are true and $$\mathbf{R}$$ is the correct explanation of $$\mathbf{A}$$

Answer

$$\mathbf{A}$$ is false but $$\mathbf{R}$$ is true

Answer

$$\mathbf{A}$$ is true but $$\mathbf{R}$$ is false

Electrostats & Capacitance

Choose the correct answer: