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 (( R 2/ R 1)) is:

Question

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 (( R 2/ R 1)) is: (A) (n/n-1) (B) (2 n/2 n+1) (C) ( n +1/ n ) (D) (2 n+1/n)

Tardigrade Admin · Accepted Answer

Capacitance of isolated Conducting sphere =4 π ε0 R1 By enclosing inside another sphere of radius R2 text , new capacitance =(4 π ε0 R1 R2/(R2-R1)) Given: (4 π ε0 R1 R2/(R2-R1))=n × 4 π ε0 R1 ⇒ ( R 2/( R 2- R 1))= n ⇒ (( R 2/ R 1)/(( R 2) R 1-1))= n ⇒ ( R 2/ R 1)= n ( R 2/ R 1)- n ⇒ ( R 2/ R 1)=( n /( n -1))

Q. 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 $(\frac{R _{2}}{R _{1}})$ is:

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

$\frac{2 n}{2 n + 1}$

$\frac{n + 1}{n}$

$\frac{2 n + 1}{n}$

Q. 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 (R1​R2​​) is:

n−1n​

2n+12n​

nn+1​

n2n+1​

Q. 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 $(\frac{R _{2}}{R _{1}})$ is:

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

$\frac{2 n}{2 n + 1}$

$\frac{n + 1}{n}$

$\frac{2 n + 1}{n}$