Question

Capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth The ratio of their radii $\left(\frac{ R _2}{ R _1}\right)$ is:

• A. $\frac{n}{n-1}$
• B. $\frac{2 n}{2 n+1}$
• C. $\frac{ n +1}{ n }$
• D. $\frac{2 n+1}{n}$

Answer 1

Answer: (A)

$\frac{n}{n-1}$

Answer 2

Capacitance of isolated Conducting sphere
=4πε0​R1​
By enclosing inside another sphere of radius
R2​, new capacitance =(R2​−R1​)4πε0​R1​R2​​
Given : (R2​−R1​)4πε0​R1​R2​​=n×4πε0​R1​
⇒(R2​−R1​)R2​​=n⇒(R1​R2​​−1)R1​R2​​​=n
⇒R1​R2​​=nR1​R2​​−n⇒R1​R2​​=(n−1)n​