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Mobile Studio (MS) Lab8
RC Circuits and Time Constant
Student name:
10/08/2017
Introduction:
RC circuit is first order linear circuit that responds to alternating current signals. The
response to different frequencies depends on the capacitance and resistance used in the
circuit.
Our objective in this lab is to stud charging and discharging of capacitors and the growth
and the decay of currents in the RC circuits.
Theory:
The time constant of a circuit is defined as: the time required for the response to decay
by a factor of 1/e (1/e= 0.3678) of its initial value. This implies that the time constant is
the time required for the response to decay to 37% of the initial value. We can make the
assumption that after 5 time constants (e-5= 0.00674) the stored voltage in the capacitor
is fully discharged because its final value is less than 1% of this initial value and the circuit
reaches its final (or steady) state. This is known as the “5 tau rule”.
Figure 1: Simple RC Circuit
Equipment:
1234-
Variable resistor (10Kohm Potentiometer).
Capacitor (C = 1 uF).
A square wave source with a peak voltage of Vpp = 1.5 Vpp and a frequency = 250 Hz.
Digital Multi-Meter (DMM).
Procedures:
1- Build the RC circuit, with the resistor R replaced by a variable resistor (10Kohm
Potentiometer) and C = 1 uF. Assume the source is a square wave with a peak
voltage of Vpp = 1.5 Vpp and a frequency = 250 Hz. Connect your input AWG1 to
Node A and measure the output A2SE by connecting it to Node B.
2- Start varying the value of R using the potentiometer. Next, capture and save the
output observed at node B, with channel#1 showing Vin (square wave) and
channel#2 showing Vout (across the capacitor). Make sure you select the AWG1
input for channel 1 and the A2SE input for channel 2.
Analysis of Results: To predict the value of R
3- Look at the screen capture for the capacitor voltage Vout and determine how long it
takes for the capacitor to fully discharge by measuring the time on the X-axis.
4- Compute the time constant of your circuit using the “5 tau rule”.
5- Predict the value of the variable resistor R Using the calculated valunie of the time
constant.
6- Carefully remove the variable resistor from the circuit (without touching the wiper
handle) and measure the actual value of the resistor using a DMM.
7- Compare the predicted value and the measured value of R and calculate error
percentage.
8- Replace the C = 1 uF capacitor by a new C = 0.47 uF capacitor and repeat all the
steps (3-7).
9- Step#9: Replace the C = 1 uF capacitor by a new C = 2.2 uF capacitor and repeat all
the steps (3-7).
Results:
Figure 2: Wave Form
1- For c= 1 uF:
- From the screen, it took the capacitor 2 ms to fully discharge.
- Using 5 tau rule: assume the time constant is τ.
τ= time of 𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 to time of
𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙
2τ= time of 𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 to time of
𝑒
𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙
𝑒2
Also, 5τ= time of 𝑉𝑖𝑛𝑖𝑡𝑖𝑎𝑙 to time of
So, 2 ms is 5 time constants.
2
5τ=2 ...