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In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.

The expression and the region of convergence of the z-transform of the sampled signal are

- $\frac{5 z}{z-e^{-5}},|z|<e^{-5}$
- $\frac{5 z}{z-e^{-0.05}},|z|<e^{-0.05}$
- $\frac{5 z}{z-e^{-0.05}},|z|>e^{-0.05}$
- $\frac{5 z}{z-e^{-5}},|z|>e^{-5}$