An introduction to electrical circuits, and their use in physiology
Resistors in series, and the potential divider circuit
Imagine
a circuit similar to the one considered previously, but with
two resistors in it instead
of one. The two resistors are said to be arranged in series, because electrons
leaving the battery have to pass through both in turn in order
to get back to the battery (remember that we can assume that
no current
flows through a voltmeter). The total resistance in the circuit
is given simply by (R1 + R2),
because the battery has to push current through both in turn.
The diagram shows three voltmeters connected into the circuit
- one is
measuring the voltage V1 across
resistor R1,
one is measuring voltage V2 across
resistor R2,
and the third is measuring the voltage V3 across
both resistors.
For the same reasons as presented previously, you should be able to see that the voltage V3 across both resistors must be the same as the voltage across the battery, the "total voltage" in the circuit (this is 3V, if we use the same battery as before). The current, I, has to pass through both resistors, so I must be the same everywhere. We can write down three equations based on Ohm's law:
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V1 = I.R1 V2 = I.R2 V3 = I.(R1 + R2) |
(1) (2) (3) |
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We can use Equations (1) and (3) to eliminate I, whereupon we can see that: |
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V1/R1 = V3 / (R1 + R2) |
(4) |
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...which, when rearranged, gives us: |
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V1/V3 = R1 / (R1 + R2) |
(5) |
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Since (R1 + R2) is the total resistance in the circuit, and V3 is the "total voltage" produced by the battery, Equation (5) shows us that the fraction of the total voltage across a given resistor in a series circuit is equal to the fraction of the total resistance which that resistor represents. The bigger the value of a given resistor, the bigger the share of the total voltage across it, i.e. the larger the drop in potential between one side of the resistor and the other. The same applies to any number of resistors arranged in series: the voltage across each one will be in proportion to its size relative to the total resistance.
The circuit shown is referred to as a potential divider: the total voltage (potential) produced by the battery is divided between each of the resistors, according to their relative sizes. In our experimental practical classes, we will use a potential divider circuit to calculate an unknown resistance which cannot be measured directly. Imagine that we wanted to know the resistance R2. If we knew the overall voltage produced by the battery, which would be equal to V3, and if we could measure the voltage V1 across a known resistance R1, we could rearrange Equation (5) to work out the value of the unknown resistance R2. In our practical, we do this in order to work out the resistance of an artificial membrane, but the same principle could be applied to work out the resistance of a real cell membrane.
If there are other physics-related areas that you would like to see introduced in a similar way on-line, please contact Dr Matt Mason