Module 1_4_6 | MIT 8.02SC Physics II: Electricity and Magnetism, Fall 2010


Uploaded by MIT on 29.12.2010

Transcript:

27-24.
We charge a capacitor 'C', and we charge it to 15 volts.
Then we discharge it through a resistor 'R'.
So here is that capacitor, it's fully charged, switch
here, resistor here, 'R', throw the switch-- at first
there is +15 volts here--
we throw the switch, current is going to flow until the
capacitor is completely discharged.
Now this 'R' is part of a voltmeter.
I shall call it 'Rv', and that is 2.25 times 10 to the sixth
ohms. And what the voltmeter indicates--
this is really a voltmeter--
is, of course, the product of the current through the
voltmeter times the resistance of the voltmeter.
So that's what the reading will show you.
You start throwing the switch.
What do you see?
15 volts, of course.
Now you wait 5 seconds and what do you see?
You only see 1/3 of 15 volts.
You only see 5 volts.
At least that's a given.

Well, if you look in your book at page 848 you see in detail
how we set up the differential equations for this circuit.
It's extremely simple.
And you'll find then that the current through this circuit,
going in this direction, has a function of time equals 'i0'
times 'e' to the ''- t' divided by 'RC''.
Sometimes 'RC' is called the discharge time, which is, of
course, a little bit of a jargon.
Because it takes infinitely long for the whole thing to be
discharged.
You have to wait for t infinitely long for the
current to become 0.
Now, the voltmeter reads 'i' times 'R'.
'i' times 'R'.
But since you have the 'R' on the right side as well as on
the left side, that's fine.
You can ignore that.
What you do know, however, is that after 5 seconds it over
'i0' is 1/3.
So 1/3 equals 'e' to the ''- t' over 'RC'.
't' is 5 seconds over 'RC'.

Well, you know 'R'.
2.25 megaohms. So out pops 'C'.
And I found that 'C' equals 2 microfarads.
If you make a curve of the current as a function of time,
that would look like this.
This is the current, this is the time, you start off with
some current 'i0', and it discharges in exponential
fashion, and by the time it is down to 'i0' over 'e', which
is somewhere here, the time 't' equals 'RC'.
That's why it's often called the 'RC' time of the circuit.