Find the time constant for the given RC circuits in correct order (in `mus`)
`R_(1)=1Omega,R_(2)=2Omega,C_(1)=4muF,C_(2)=2muF`

Options

A. `18,4,(8)/(9)`
B. `18,(8)/(9),4`
C. `4,18,(8)/(9)`
D. `4,(8)/(9),18`

Answer

B

Explanation

`tau=CR`
`tau_(1)=(C_(1)+C_(2))(R_(1)+R_(2))=18mus`
`tau_(2)=((C_(1)C_(2))/(C_(1)+C_(2)))(R_(1)R_(2))/(R_(1)+R_(2))=(8)/(6)xx(2)/(3)=(8)/(9)mus`
`tau_(3)=(C_(1)+C_(2))((R_(1)R_(2))/(R_(1)+R_(2)))=(6)((2)/(3))=4mus`