Download RC time constants

RC TIME CONSTANTS
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When a capacitor is charged or discharged
through a resistor, the time taken to charge
the capacitor depends upon the value of the
resistor and capacitor. This is known as the
RC time constant. This module explains
how the RC time constant is measured and
how to work out long it will be.
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The circuit (left) shows a
resistor and capacitor
connected together to form an
RC time constant.
When the power (Vin) is
connected, current will start
to flow through the resistor
into the capacitor.
As this happens the capacitor
will start to charge and Vcap
will begin to rise.
The bigger the resistance the
more the current is limited
and the longer the capacitor
takes to charge. Also the
bigger the capacitor the
longer it takes to charge.
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The graph on the left shows
how the voltage across the
capacitor increases with time.
On the graph you will see that
to start with the capacitor
charges quickly, but then as it
gets more and more full of
charge the rate it charges at
gets less and less.
Mathematically speaking the
capacitor never quite reaches
fully charged, however in
practice it gets so close to
being fully charged we
couldn't tell.
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Since the capacitor never
fully charges we can't
measure the time taken to
charge. Instead we measure
the time (Trc on the graph)
taken for the capacitor to
reach 70% of its final voltage.
We have already stated that
the time constant (T) is longer
if either the resistance (R) or
capacitance (C) are bigger.
The time to charge the
capacitor to 70% of its final
voltage is:
T = RC
So to get the time constant we
just multiply the resistance
by the capacitance.
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Before we look at an example, let's just remind
ourselves of units of resistance & capacitance.
With the capacitors we will mainly be using
capacitors measured in micro Farads (uF)
unless we want a time constant of a fraction of a
second.
Looking at the circuit on
the left:
 R = 1M
 C = 1 uF
 As T = R C
 T = 1M x 1uF
 T = 1,000,000 x 0.000001
 T = 1 second
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Normally we have a time constant
we would like to achieve and have
selected either a resistor or
capacitor value. We then need to
work out the value of the
remaining part.
Take the example on the left,
suppose we want a time constant
of 30 seconds and have selected a
220 uF capacitor. Then we can
work out the resistor (R) using:
R=T/C
R = 30 / 0.000220
R = 136 K (in practice we would
need to use a preferred value - say
150 K)