# Task 5.11: Capacitor and RC Characteristics > [!figures] Figure I: RC Circuit Schematic > ![[Pasted image 20261009171433.png|center|400]] > [!calculation] Time Constant Calculation & Percent Error > $R=10k\Omega,\qquad C=100\mu F=1\times10^{-4}F$ > $\tau_{calc}=RC=(10,000)(1\times10^{-4})=1.000s$ > $\tau_{meas}=0.953125s$ > $\%\text{ error}=\left|\frac{\tau_{meas}-\tau_{calc}}{\tau_{calc}}\right|\times100$ > $=\left|\frac{0.953125-1.000}{1.000}\right|\times100=\boxed{4.69\%}$ > [!table] Table I: Calculated vs. Measured RC Time Constant > > | Calculated $\tau$ (s) | Measured $\tau$ (s) | Percent Error | > | ---: | ---: | ---: | > | 1.000 | 0.953 | 4.69% | > [!figures] Figure II: Resistor Voltage During Capacitor Charging > ![[Pasted image 20261009172034.png|center|450]] > [!figures] Figure III: Voltage Across Each Component During Charging > ![[Pasted image 20261009172046.png|center|450]] > [!calculation] Capacitor Voltage from Oscilloscope Measurements > Using Kirchhoff's Voltage Law: > $V_s=V_R+V_C$ > $\boxed{V_C(t)=V_s(t)-V_R(t)}$ > > The theoretical charging equations are: > $V_C(t)=V_s(1-e^{-t/RC})$ > $V_R(t)=V_se^{-t/RC}$ > [!figures] Figure IV: Resistor Voltage with a 2.5 V Source > ![[Pasted image 20261009172110.png|center|450]] > [!figures] Figure V: RC Charging Curves with a 2.5 V Source > ![[Pasted image 20261009172122.png|center|450]] > [!calculation] Time Constant with 2.5 V Source > $\tau_{calc}=RC=1.000s$ > $\tau_{meas}\approx1.008s$ > $\%\text{ error}\approx\left|\frac{1.008-1.000}{1.000}\right|\times100=0.8\%$ > [!note] Step 7: Observations > - Capacitor voltage increases toward 2.5 V rather than 5 V. > - Resistor voltage decreases toward 0 V. > - Voltage magnitudes are approximately half those observed with the 5 V source. > - The time constant remains approximately 1 second. > - Changing the source voltage does not change the RC time constant because $\tau=RC$ depends only on resistance and capacitance. # Task 5.12: De-bouncing a Switch > [!figures] Figure VI: Pull-Down Switch Circuit Schematic > ![[Pasted image 20261009172321.png|center|300]] > [!note] Pull-Down Circuit Behavior > - $R=10k\Omega$ > - Switch open: $V_{out}=0V$ (LOW). > - Switch closed: $V_{out}=V_{in}=5V$ (HIGH). > - The resistor provides a path to ground when the switch is open, preventing a floating output. > [!figures] Figure VII: Switch Bouncing in a Pull-Down Circuit > ![[Pasted image 20261009172333.png|center|450]] > [!figures] Figure VIII: Pull-Down Circuit with Reduced Switch Bouncing > ![[Pasted image 20261009172442.png|center|300]] > [!calculation] RC Time Constant for Debouncing > $R=10k\Omega,\qquad C=0.1\mu F$ > $\tau=RC=(10,000)(0.1\times10^{-6})$ > $\boxed{\tau=1ms}$ > [!note] Step 6: Response-Time Tradeoff > - Increasing capacitance reduces phantom lines but increases the response time. > - Smaller capacitance allows faster switching but may not sufficiently suppress bouncing. > - An appropriate RC combination balances signal stability and responsiveness. > > **Selected combination:** > - $R=10k\Omega$ > - $C=0.1\mu F$ > [!figures] Figure X: Pull-Up Switch Circuit Schematic > ![[Pasted image 20261009172506.png|center|450]] > [!note] Pull-Up Circuit Behavior > - Switch open: $V_{out}=V_{in}=5V$ (HIGH). > - Switch closed: $V_{out}=0V$ (LOW). > - The resistor provides a path to the supply when the switch is open. > - The output behavior is reversed compared with the pull-down circuit. > [!figures] Figure XI: Switch Bouncing in a Pull-Up Circuit > ![[Pasted image 20261009172526.png|center|450]]