Introduction
Ti me Constant (τ): A measure of time required for certain changes in voltages and currents in RC
and RL circuits. Generally, when the elapsed time exceeds five time constants (5τ) after switching has occurred, the currents and voltages have reached their final value, which is also called steadystate response.
The time constant of an RC circuit is the product of equivalent capacitance and the Thévenin resistance as viewed from the terminals of the equivalent capacitor.
τ RC =
A Pu l se is a voltage or current that changes from one level to the other and back again. If a
waveform’s hight time equals its low time, as in figure, it is called a square wave. The length of each cycle of a pulse train is termed its period its period (T).
The pulse The pulse width (t ) of an ideal square wave is equal to half the time period. p
The relation between pulse width and frequency is t hen given by,
From Kirchoff’s laws, it can be shown that the charging voltage V (t) across the capacitor is given C
by: -t /RC /RC
V (t) =V =V ( 1- e C
)
t≥0 1
Objective
1. To determine RC circuit configuration. 2. To measure time constant of an RC Circuit
Equipment/Component List
Power supply 5v, breadboard, multimeter, Oscilloscope, function generator, resistors 500Ω, 5KΩ, 1MΩ, capasitor 1µF, 220µF.
(i) Determining the RC Circuit Configuration
Procedure 1
1. Build the circuit shown in Figure on the breadboard mounted to the bench top. 2. Let R = 5 K Ω and C = 220 µF. 3. Measure and record the R L from the ohmmeter.
Measured Result
The value of the resistor not be able to measure. This is because when I connect a current source using DC, the capasitor is always open circuit. There are no current flows through the capasitor because it connected in series with resistor. No current and voltage flow in this circuit.
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Procedure 2
1. Build the circuit shown in Figure on the breadboard mounted to the bench top. 2. Let R = 5 K Ω and C = 220 µF. 3. Measure and record the R L from the ohmmeter.
Measured Results
The value of the resistor reading from ohmmeter is 5K Ω. The values able to measure because when I connect a current source using DC, the capasitor is always open circuit, but the resistor and capasitor are connected in parallel so, there will have a voltage and current flowing through the resistor.
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(ii) Measuring Time Constant of an RC Circuit
Procedure 3
1. Build the circuit shown in Figure on the breadboard mounted to the bench top. 2. Let R = 1 MΩ and C = 1 µF. 3. Set the pulse amplitude to 1-V and increase the pulse width while displaying Vin and Vo on the oscilloscope. The repetition rate may need to be adjusted. Be sure that the time between pulses is long enough so that no charge is left on the capacitor at the beginning of the next pulse. 4. Sketch this response. 5. Extrapolate the initial slope with a straight line until it intersects 1 V. Then drop a vertical line from the point where the straight-line extrapolation intersects the input voltage. Compare this time difference to one RC constant.
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Result
The scope adjusted to 250 ms/Div scale for X-axis and 1mV for Y-axis. The actual time constant, τ is 1 second. τ = RC 1 MΩ x 1 µF = 1 second
-1
At one time constant, the value has dropped by VP * (1 - e ). Hence, referring to Figure, at time T2, the voltage approximately 0.63 V. From the plot, 5τ are required before the capasitor has fully charged.
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Discussion and Conclusion
In conclusion, this report details the successful application of an experimental method for determine RC circuit configuration and measure time constant of an RC Circuit. Between parallel and series circuit, voltage and current will flow through the parallel circuit. In measured time constant of an RC, the output voltage approximately 0.63V. 5τ are required before the capasitor has fully charged. Time constant are successfully verified by this circuit.
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