The earth has volume V and surface area A, then capacitance would be

Question

The earth has volume V and surface area A, then capacitance would be (A)  4π ε 0(A/V)  (B)  4π ε 0(V/A)  (C)  12π ε 0(V/A)  (D)  12π ε 0(A/V)

Tardigrade Admin · Accepted Answer

Volume of sphere (earth) =(4/3)π R3 Where R is the radius of the sphere. Area of the sphere =4π R2 Now, (V/A)=(R/3) ?(i) Capacitance of a sphere C=4π ε 0R ...(ii) From Eqs. (i) and (ii), we get C=4π ε 0( (3V/A) )=(12π ε 0V/A)

Q. The earth has volume V and surface area A, then capacitance would be

$4 π ε_{0} \frac{A}{V}$

$4 π ε_{0} \frac{V}{A}$

$12 π ε_{0} \frac{V}{A}$

$12 π ε_{0} \frac{A}{V}$

Q. The earth has volume V and surface area A, then capacitance would be

4πε0​VA​

4πε0​AV​

12πε0​AV​

12πε0​VA​

Volume of sphere (earth) =34​πR3 Where R is the radius of the sphere. Area of the sphere =4πR2 Now, AV​=3R​ ?(i) Capacitance of a sphere C=4πε0​R ...(ii) From Eqs. (i) and (ii), we get C=4πε0​(A3V​)=A12πε0​V​

$4 π ε_{0} \frac{A}{V}$

$4 π ε_{0} \frac{V}{A}$

$12 π ε_{0} \frac{V}{A}$

$12 π ε_{0} \frac{A}{V}$