A) 10 second
B) 5 second
C) 2.5 second
D) 20 second
Correct Answer: C
Solution :
| [c] Time constant for parallel combination = 2RC |
| Time constant for series combination \[=\frac{RC}{2}\] |
| In first case: |
| \[V={{V}_{0}}{{e}^{\frac{{{t}_{1}}}{2RC}}}=\frac{{{V}_{0}}}{2}\] ..(i) |
| In second case: |
| \[V={{V}_{0}}{{e}^{-\frac{{{t}_{2}}}{(RC/2)}}}=\frac{{{V}_{0}}}{2}\] (ii) |
| From (i) & (ii), |
| \[\frac{{{t}_{1}}}{2RC}=\frac{{{t}_{2}}}{(RC/2)}\] \[\Rightarrow \] \[{{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{10}{4}=2.5\sec .\] |
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