A capacitor of capacitance `2muF` is charged to a potential difference of `5V`. Now, the charging battery is disconected and the capacitor is connected in parallel to a resistor of `5Omega` and another unknown resistor of resistance `R` as shown in figure. If the total heat produced in `5Omega` resistance is `10muJ` then the unknown resistance `R` is equal to

Options

A. `10Omega`
B. `15Omega`
C. `10/3Omega`
D. `7.5Omega`

Answer

C

Explanation

Total heat produced `=1/2CV^2`
`=1/2(2muF)(5)^2`
`=2muJ`
Now this should distribute in inverse ratio of resistors, as they are in parallel.
`:. H_(5Omega)/H_R=R/5`
or `H_(5Omega)=(R/(R+5))` (total heat)
`or 10=(R/(R+5))(25)`
Solving this equation, we get
`R=(10/3)Omega`