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In last week's lab we looked at purely resistive circuits-- circuits made of only a battery
and an effective resistance-- and saw that at some voltage, a big resistance meant a
small current.
We also looked at purely capacitive circuits, where we found that a big capacitance meant
we could build up a big charge, Q, at some constant voltage.
In this week's lab, we will combine both resistors and capacitors in series in the same circuit,
and we'll find that we now have a circuit where the voltage across either the capacitor
or resistor changes with time.
So let's imagine that we just connected this circuit-- current has started flowing but
hasn't built up charge on the capacitor plates yet. So the voltage across the capacitor is
zero. And the entire potential difference from the battery is dropped across the resistor.
This is the maximum voltage we'll have across the resistor, so the current in the circuit
will start out at a maximum.
To understand what happens as time goes on, we'll need to have a good picture of where
the charge is, and where it's flowing. Initially everything starts with a net neutral charge.
The positive charges are stationary, but the negative charges can flow through the battery
from its more positive to more negative side.
All of this current just starts to build up a net charge difference on the capacitor,
which means the voltage across the capacitor starts to increase. Then less voltage is left
to be dropped across the resistor, and the current through the resistor starts to decrease.
And this keeps going on-- current flows through the resistor and builds up charge on the capacitor.
So the voltage across the capacitor increases, and the voltage left to drop across the resistor
decreases. So the current decreases, and charge builds up more slowly. Eventually, the right
amount of charge will be built up on the capacitor such that the voltage across the capacitor
is just the voltage across the battery. Then there's a zero voltage difference across the
resistor, and no more current flows.
If you consider very small time intervals, you'd get a smooth function for the voltage
versus time that looks like this.
At this point we say the capacitor is charged-- we can even remove the battery, and that net
charge difference will remain across the capacitor.
In the last part of this lab, we'll build a more complicated RC circuit to model the
electrical properties of a cell membrane. But while that circuit looks complex, it is
really just this basic RC unit repeated over and over-- where the voltage across the capacitor
of one unit becomes the voltage supply of the next, and we'll see how charge will propagate
as a pulse from one of these RC units to the next.
This week you'll use a lot of the same equipment and techniques as in the last circuits lab--
the main difference is that you'll use the computer's data acquisition system to take
fast voltage measurements versus time.
You'll use this pulse generator to create short voltage pulses. It connects to your
voltage source leads on one side, and outputs a pulse on the other side when you press the
button on top.
Here's the whole RC circuit-- pulse generator, with a resistor, capacitor and wire across
its output. When you're modeling the cell membrane, you'll connect more resistors and
capacitors like so.
To make a measurement in DataStudio, you'll need to tell the computer to start taking
data when you press the pulse generator button. So the first set of leads will connect to
the pulse generator output and channel A of the data acquisition box to trigger the measurement.
The other sets of leads you'll place across capacitors farther down the line to observe
pulse propagation down the RC circuit.