# Lab 13: The Response of an RC Circuit

## Objectives

• Validate the R-C response for a partially and fully charging/discharging capacitor.
• Check the validity of Kirchhoff’s Voltage Law for an R-C circuit.

## Background

Consider the Thévenin RC circuit with the square wave voltage input. The time dependent voltage across the capacitor is:

$$\begin{array}{l} {v_C}(t) = {V_{OC}} + \left( {{v_c}({0^ - }) - {V_{OC}}} \right) \times {e^{ - t/\tau }} \equiv {V_{final}} + ({V_{initial}} - {V_{final}}) \times {e^{ - t/\tau }}\\ \end{array}$$

What determines whether a capacitor is partially or completely charged is the pulse width (pw) of the square wave input. Two cases will be considered:

1. pw = 5τ and
2. pw = 2.

For a pulse width of or greater, the capacitor will have enough time to completely charge up and completely discharge.

For a pulse width of , the capacitor will not have had enough time to completely charge up or completely discharge. It will require 5 cycles of the constant square wave input to reach its final steady state value. The repeated application of the complete response for a constant input for these 5 cycles will ultimately achieve the final steady-state value that is observed experimentally on the oscilloscope.

## Procedure

Part 1: Setting up the Function Generator

## Questions

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