Step-by-step explanation:
It is given that,
The time constant of RC circuit,
![\tau=0.2\ \mu s=0.2* 10^(-6)\ s](https://img.qammunity.org/2020/formulas/physics/college/hn9y3kaalqufl6ead7tiaprdsxdwjmsq2s.png)
(a) The resistance of the flash lamp is 0.0410 Ω
We know that the relation between the resistance and time constant is given by :
![\tau=R* C](https://img.qammunity.org/2020/formulas/physics/college/obxzdugobqj2d7nxm5ydl7h3iy84m3tvgu.png)
![C=(\tau)/(R)](https://img.qammunity.org/2020/formulas/physics/college/81q1ox0pdjz5n3fa61m747fnmlpxhd7s2s.png)
![C=(0.2* 10^(-6))/(0.0410)](https://img.qammunity.org/2020/formulas/physics/college/3ffalgap1pftermqgml9ac2iu3jhtm46hl.png)
![C=4.87* 10^(-6)\ F](https://img.qammunity.org/2020/formulas/physics/college/dwqnguc6o8zywtqejt83xg8ypeswsu5hqt.png)
(b) If he value of resistance,
![R=650\ k\Omega=650* 10^3\ \Omega](https://img.qammunity.org/2020/formulas/physics/college/hwho2e0gq6na8rbpa4v7yjqrl9jsoziypj.png)
![\tau=R* C](https://img.qammunity.org/2020/formulas/physics/college/obxzdugobqj2d7nxm5ydl7h3iy84m3tvgu.png)
![\tau=650* 10^3* 4.87* 10^(-6)](https://img.qammunity.org/2020/formulas/physics/college/v482pf936ppfudsx2ds48hv1sf8nwywdjl.png)
![\tau=3.16\ s](https://img.qammunity.org/2020/formulas/physics/college/ng43euygvw8ojd8olx0mafiyy6dw9uf1lw.png)
Hence, this is the required solution.