There are two concentric conducting shells of radius `R, 2R` respectively. Charge on each surface is as shown in the figure.
Equivalent capacitance of this system is:

Options

A. `A. 4piepsilon_(0)R`
B. `B. 8piepsilon_(0)R`
C. `C. 16piepsilon_(0)R`
D. `D. 12piepsilon_(0)R`

Answer

A

Explanation

This is series combination of a spherical capacitor and an isolated sphere.
Capacitance of spherical capacitor `=(4piepsilon_(0)2R^(2))/(2R-R)`
`C_(1)=8piepsilon_(0)R`
Capacitance of isolated sphere `C_(2)=8piepsilon_(0)R`
Capacitance of system is `1/C=1/(C_(1))+1/(C_(2))`
`1/C=1/(8piepsilon_(0)R)+1/(8piepsilon_(0)R)=1/(4piepsilon_(0)R)`