In a long p-type Si-bar with cross-sectional area = 0.5 $$cm^{2}$$ and $$ N_{a}.= 2 \times 10^{17} cm^{-3}$$ extra holes $$10^{16} cm^{-3}$$ are injected Assume $$\mu_{p}=500 \frac{cm^{2}}{Vs}$$, $$n_{i}=10^{10} cm^{-3}$$ and $$ \tau_{p}= 10^{-10}s $$find minority carrier lifetime.

A

$$ 10 \mu s $$

B

$$ 15 \mu s $$

C

$$ 20 \mu s $$

D

$$ 25 \mu s $$