Question: What is the formula for the time response of a first-order RC circuit to a step input?

Options:

1. V(t) = V_final(1 - e^(-t/τ))
2. V(t) = V_final(e^(-t/τ))
3. V(t) = V_initial + (V_final - V_initial)(1 - e^(-t/τ))
4. V(t) = V_initial + (V_final - V_initial)e^(-t/τ)

Correct Answer: V(t) = V_initial + (V_final - V_initial)(1 - e^(-t/τ))

Solution:

The time response of a first-order RC circuit to a step input is given by V(t) = V_initial + (V_final - V_initial)(1 - e^(-t/τ)).