Hydrology Field Methods
Wheatstone Bridge Measurements
General Information:
- Many types of equipment require the measurement of a resistance.
- Dataloggers are not directly able to measure resistance, they only measure voltage.
- Bridges are used to convert resistance to voltages.
Half-bridges
- Ohm's law, V = I R, relates a voltage drop, V, to resistance, R, where I is the current.
- If R1 = V1 / I1 is the unknown resistance we wish to measure, we just need to know the current.
- We place a known resistance, R2, in series and measure the voltage drop across it, V2, to find the current, I2
- Because the flow is in series, I1 = I2, which leads to
- V1 / R1 = V2 / R2
- because I = V / R
- We can use the total voltage, V = V1 + V2, instead of V2, yielding V2 = V - V1, so that
- This is called a half-bridge, and requires a known resistor, R2, a known total excitation voltage, V, and measured voltage drop, V1, across the unknown resistor.
Resistor Table:
| Color |
Digit (zeros) |
Multiplier |
| Silver |
(-2) |
0.01 |
| Gold |
(-1) |
0.1 |
| Black |
0 |
1 |
| Brown |
1 |
10 |
| Red |
2 |
100 |
| Orange |
3 |
1K |
| Yellow |
4 |
10K |
| Green |
5 |
100K |
| Blue |
6 |
1M |
| Violet |
7 |
10M |
| Grey |
8 |
100M |
| White |
9 |
1G |
Wheatstone (Full) Bridges
- Better accuracy can be obtained if a reference voltage is generated that is approximately equal to the voltage between the reference and unknown resistance.
- To create this reference voltage, we use two more resistors, each with a known resistance.
- Using ohms law, and given two reference resistors, R3 and R4, we have:
- Solving for V3, we have:
- We measure V = V1 - V3, so that V1 = V3 + V (and assuming that V = 2 V3)
- This technique provides more accurate estimates than the half-bridge method.
Problems:
- Resistances:
- Using two resistors: What is the total resistance a) in parallel? b) in series?
- What is the current through each circuit?
- Half-Bridges:
- Design and build a half-bridge circuit that determines an unknown resistance using a voltage measurement.
- Compare your calculated with the known resistance.
- Full-Bridges:
- Design and build a full-bridge circuit that determines an unknown resistance using a voltage measurement.
- Compare with the half-bridge method and known resistance.