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 ?, and the capacitance is very small, say, 10-12 F (1 picofarad, pF). If the capacitor is initially uncharged and the transmitting gate changes instantaneously from 0 to 5 V, how long will it take for the voltage at the receiving gate to reach (say) 3 V? (This is the time it takes to transmit a logical “1.”)

SOLUTIONStep 1Given capacitance C = Resistance R = Initial charge Voltage supplied to the circuit (E) = 5vStep 2Consider the equation…… (1)But we have Then (1) becomes ……..(2)This is linear differential equation.Step 3Integrating factor is Multiplying (2) by we getStep...