Topic: Network Theory
If the step response to the input step amplitude of 1 V is given by $V_{o}(t)=(1-e^{-t/RC})$, the network can be represented by
- A. $V_{i}$ $V_{0}$
- B. $V_{i}$ CR $V_{0}$
- C. $V_{i}$ RV $V_{0}$
- D. $V_{i}$ RC WE $V_{0}$
Answer: A. $V_{i}$ $V_{0}$
Explanation: $V_{o}(t)=(1-e^{-t/RC})$, $V_{i}(t)=1~V$. Taking the Laplace T/F of equation (i) $V_{O}(s)=\frac{1}{s}-\frac{1}{s+\frac{1}{RC}} = \frac{1}{s(RCs+1)}$. $V_{i}(s)=\frac{1}{s}$ (Taking the Laplace of equation (ii)). $\frac{V_{o}(s)}{V_{i}(s)}=\frac{1}{RCs+1}$. It can be represented as an RC low pass network with R in series and C in parallel.