Wheatstone bridge
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![A Wheatstone bridge has four resistors forming the sides of a diamond shape. A battery is connected across one pair of opposite corners, and a galvanometer across the other pair.](http://upload.wikimedia.org/wikipedia/commons/thumb/9/93/Wheatstonebridge.svg/300px-Wheatstonebridge.svg.png)
A Wheatstone bridge is an
The Wheatstone bridge was invented by
Operation
In the figure, Rx is the fixed, yet unknown, resistance to be measured. R1, R2, and R3 are resistors of known resistance and the resistance of R2 is adjustable. The resistance R2 is adjusted until the bridge is "balanced" and no current flows through the
At the point of balance,
Detecting zero current with a galvanometer can be done to extremely high precision. Therefore, if R1, R2, and R3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected.
Alternatively, if R1, R2, and R3 are known, but R2 is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of Rx, using Kirchhoff's circuit laws. This setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.
Derivation
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Wheatstonebridge_current.svg/300px-Wheatstonebridge_current.svg.png)
Quick derivation at balance
At the point of balance, both the voltage and the current between the two midpoints (B and D) are zero. Therefore, I1 = I2, I3 = Ix, VD = VB.
Because of VD = VB, then VDC = VBC and VAD = VAB.
Dividing the last two equations by members and using the above currents equalities, then
Full derivation using Kirchhoff's circuit laws
First,
Then, Kirchhoff's second law is used for finding the voltage in the loops ABDA and BCDB:
When the bridge is balanced, then IG = 0, so the second set of equations can be rewritten as:
Then, equation (1) is divided by equation (2) and the resulting equation is rearranged, giving:
Due to I3 = Ix and I1 = I2 being proportional from Kirchhoff's First Law, I3I2/I1Ix cancels out of the above equation. The desired value of Rx is now known to be given as:
On the other hand, if the resistance of the galvanometer is high enough that IG is negligible, it is possible to compute Rx from the three other resistor values and the supply voltage (VS), or the supply voltage from all four resistor values. To do so, one has to work out the voltage from each
where VG is the voltage of node D relative to node B.
Significance
The Wheatstone bridge illustrates the concept of a difference measurement, which can be extremely accurate. Variations on the Wheatstone bridge can be used to measure
The concept was extended to alternating current measurements by James Clerk Maxwell in 1865[4] and further improved as Blumlein bridge by Alan Blumlein in British Patent no. 323,037, 1928.
Modifications of the basic bridge
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Kelvin_bridge_by_RFT.png/300px-Kelvin_bridge_by_RFT.png)
The Wheatstone bridge is the fundamental bridge, but there are other modifications that can be made to measure various kinds of resistances when the fundamental Wheatstone bridge is not suitable. Some of the modifications are:
- Carey Foster bridge, for measuring small resistances
- Kelvin bridge, for measuring small four-terminal resistances
- Maxwell bridge, and Wien bridge for measuring reactive components
- Anderson's bridge, for measuring the self-inductance of the circuit, an advanced form of Maxwell's bridge
See also
- Diode bridge, product mixer – diode bridges
- Phantom circuit – a circuit using a balanced bridge
- Post office box (electricity)
- Potentiometer (measuring instrument)
- Potential divider
- Ohmmeter
- Resistance thermometer
- Strain gauge
References
- ^ "Circuits in Practice: The Wheatstone Bridge, What It Does, and Why It Matters", as discussed in this MIT ES.333 class video
- .
- 's contributions, and why the bridge carries Wheatstone's name.
- ^ Maxwell, J. Clerk (1865). "A dynamical theory of the electromagnetic field". Philosophical Transactions of the Royal Society of London. 155: 459–512. Maxwell's bridge used a battery and a ballistic galvanometer. See pp. 475–477.
External links
Media related to Wheatstone's bridge at Wikimedia Commons
- DC Metering Circuits chapter from Lessons In Electric Circuits Vol 1 DC free ebook and Lessons In Electric Circuits series.
- Test Set I-49