Digging up the Past
1. The Secrets of Resistance

The measurement of resistance is a common technique in the physics of archaeology.  Where the resistance of the ground changes, that might well indicate something of interest to the archaeologist.

Resistivity

The resistance of any material depends on:

We can combine these to a useful expression:

 

We can rearrange this to give us:

 

The units for resistivity are ohm metres (Wm)

 

  1. The units are NOT ohms per metre.
  2. The physics code r (rho, a greek letter 'r') is sometimes confused for density.
  3. Area must be in square metres, and length in metres.

 

Typical values for resistivity are shown in the table below:

Material Resistivity (Wm)
Copper 1.7 × 10-8
Lead 2.1 × 10-7
Carbon 1.4 × 10-5
Glass 1.0 × 1012
Perspex 1.0 × 1016

Clearly conductors have low value value of resistivity.  Conductivity is the reciprocal of resistivity, and is given the physics code s (sigma, a Greek letter 's').

 

Potential Dividers

The potential divider is at its simplest two series resistors connected to a battery and the voltage is measured between the negative terminal and a point between the two resistors.

 

You can treat this circuit as two resistors in series, working out the total resistance, the current, then working out the voltage across R2.  However you can use the potential divider equation:

 

You don't have to have fixed value resistors.  Variable resistors and components like thermistors and light dependent resistors are put into potential divider circuits.  You can use a piece of resistance wire between to fixed points and move a slider to any point between them.  This is a potentiometer.

You can also measure the potential in two dimensions.

 

The orange dotted lines represent equipotentials, lines of equal potential.

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