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RC Timing Circuits

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AS A2

Time Constant: T = R C

Capacitors can be used, with a resistor, for timing.
The 555 timer relies on this.

The time constant calculations below are needed for designing timing circuits.

T is the time in seconds.
R is the resistor value in Ohms.
C is the capacitor value in Farads.

Here is a timing circuit. Click the switch the start charging or discharging ...

Advanced Science: In this circuit, when the switch is flipped, the voltage across the capacitor changes quite fast and the current flowing is larger. As the capacitor approaches full charge (or discharge) the voltage changes more slowly and the current is smaller. The current is proportional to the rate of change of voltage. This is completely unlike resistor behaviour where the current is proportional to the voltage.

RC Timing Calculations

Charging

R = 1000000 Ohms. C = 1 Microfarad. R C = 1 Second.
0%	T = 0 Seconds
50%	T = 0.69 R C Seconds
63%	T = R C Seconds
66.6%	T = 1.1 R C Seconds (555 Monostable)
100%	T = 5 R C Seconds

Discharging

R = 1000000 Ohms. C = 1 Microfarad. R C = 1 Second.
100%	T = 0 Seconds
50%	T = 0.69 R C Seconds
37%	T = R C Seconds
0%	T = 5 R C Seconds

Experiment

The aim is to measure the voltage across a charging capacitor at regular time intervals. Once the capacitor is fully charged, repeat the measurements while it is discharging. These results should be plotted on a graph. The graph should then be marked up with the key positions listed above.

R = 47kΩ
C = 2200 Microfarads.
Charge for 10 minutes. Connect the resistor to the 5 Volt supply.
Discharge for 10 minutes. Connect the resistor to the 0 Volt supply.
Don't turn off the stopwatch at half time!

Tasks

Calculate the time constant T = RC
Note that capacitors are not usually manufactured with great accuracy and DC leakage may be noticeable when you take your measurements.

Plot and Label the Graph

Charging ...

Mark the graph at the 50% mark after 0.69RC seconds
Mark the graph at the 63% mark after RC seconds
Mark the graph at the 66.6% mark after 1.1RC seconds
Mark the graph at the 100% mark after 5RC seconds

Discharging

Mark the graph at the 50% mark after 0.69RC seconds
Mark the graph at the 37% mark after RC seconds
Mark the graph at the 0% mark after 5RC seconds

Leakage

Estimate the leakage resistance of the capacitor. (This may well not be constant.)

Picoscope Traces for a Faster Timing Circuit

R = 1 kΩ
C = 0.47 µF

Falstad Simulation

For the Falstad Circuit Simulation, CTRL+Click DC RC Timing Circuit
In options, check European Resistors and uncheck Conventional Current.
Click the switch to charge and discharge the capacitor

Alternatively view RC_Timing.txt.
Save or copy the text on the web page. Import the saved or copied text into the Falstad simulator.

Here is the new HTML5 Simulator Site.

A2 ONLY: Reactance of a Capacitor

This is the AC equivalent of resistance.

Xc = 1 / ( 2 p F C )

Xc is the reactance measured in Ohms.
F is the frequency.
C is the capacitance.
Xc is inversely proportional to F (As F increases, Xc decreases).
Xc is inversely proportional to C (As C increases, Xc decreases).