Five capacitors, each of capacitance value `C` are connecteed as shown in the figure. The ratio of capacitance between `P` and `R`, and the capacitance between `P` and `Q`, is.

Options

A. `3:1`
B. `5:2`
C. `1:1`
D. `2:3`

Answer

D

Explanation

If a source is connected between points `P` and `R`, same charge will flow through two capacitors in arms `PQ` and `QR`. Similarly, same charge will flow through capacitors in arms `PT, TS` and `SR`.
So, equivalent capacitance of left side
`C' = (C xx C)/(C + C) = (C )/(2)`
and equivalent capacitances of right side
`(1)/(C'') = (1)/(C )+(1)/(C ) + (1)/(C ) = (3)/(C )`
`:. C'' = (C )/(3)`
Now, `C''` and `C''` will be in parallel combination, hence
`C_(1) = C' + C'' = (C )/(2) + (C )/(3) = (5C)/(6)`
Similarly, if a source is connected between points `P` and `Q`, then equivalent capacitance
`C_(2) = C + (C )/(4) = (5C)/(4)`
Hence, the required ratio is given by
`(C_(1))/(C_(2)) = (5C//6)/(5C//4) = (2)/(3)`