-
The output response y(t) of the RC network shown in fig. is—
-
- 1– et/RC
- 1 + e– t/RC
- 1 – e– t/RC
- 1 + et/RC
Correct Option: C
The transfer function of the network
| H(s) = | ||
| Cs | ||
| R + | ||
| Cs | ||
| = | · | |||||
| RC | s + | |||||
| RC | ||||||
Therefore, the impulse response of the network is
| h(t) = | e– t/RC for t ≥ 0 | RC |
| Given, f(t) = |  | 1, for t ≥ 0 |
| = |  | T | x(τ) h(t – τ)·dτ | 0 |
| = | | t | 1· | e– (t – τ )/RCdτ | 0 | RC |
| = | | t | eτ/RCdτ | RC | 0 |
| = | [RC·eτ/RCdt]t0 | RC |
| = | [et/RC – 1] | RC |
= 1 – e– t/RC
Hence, alternative (C) is the correct choice.
