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. `2:3`
D. `1:1`

Answer

C

Explanation

Between the points P and Q , a capacitor `C_(1)` and series combination of `C_(2),C_(3),C_(4),C_(5)` are connected in parallel.

`:. (1)/(C_(s))=(1)/(C_(2))+(1)/(C_(2))+(1)/(C_(4))+(1)/(C_(5))`
`=(1)/(c)+(1)/(c)+(1)/(c)+(1)/(c)=(4)/(c)`
or `C_(s)=C//4`
The equivalent capacitance betwen P and Q is `C'=C_(1)+C_(1)=C+(C)/(4)=(5C)/(4)`
Betwen the points P and R a series combination of `C_(1),C_(2)` and a series combination of `C_(3),C_(4),C_(5)` are connected in parallel.
`:. (1)/(C_(s))=(1)/(C_(1))+(1)/(C_(2))=(1)/(C)+(1)/(C) or, C'=(C)/(2)`
`(1)/(C_(s)^(n))=(1)/(C_(3))+(1)/(C_(4))+(1)/(C_(5))=(1)/(C)+(1)/(C)+(1)/(C)=(3)/(C) or, C''(C)/(3)`
The equivqlent capacitance between P and R is `C=C_(s)+C_(s)=(C)/(2)+(C)/(3)=(5C)/(6)`
`:. (C'')/(C'')= ((5C//6))/((5C//4))=(4)/(6)=(2)/(3)`