Chapter 3.5, Problem 3E

The pathway for a binary electrical signal between gates in an integrated circuit can be modeled as an $RC$ circuit, as in Figure 3.13(b); the voltage source models the transmitting gate, and the capacitor models the receiving gate. Typically, the resistance is $100\Omega$, and the capacitance is very small, say, ${10}^{-12}\text{F}$ $\left(1\text{picofarad,}\text{pF}\right)$. If the capacitor is initially uncharged and the transmitting gate changes instantaneously from $0$ to $5\text{V}$, how long will it take for the voltage at the receiving gate to reach (say) $3$ $\text{V}$? (This is the time it takes to transmit a logical “ $1$.”)