Weatstone Bridge

The Wheatstone Bridge circuit consists of two potential dividers connected between the supply and ground. One divider is formed from R₁ and R₂, the other from R₃ and R₄. The voltage at the point between R₁ and R₂, and that between R₃ and R₄ will vary according to the resistor value. V_bridge is the voltage between these points, as shown in the diagram below:

When the voltages are equal V_bridge will be zero, at which point the bridge is said to be balanced. At this point the value of R₄ can be found from:

R₄ = (R₃ * R₂) / R₁

A typical application for a Wheatstone Bridge is for measuring resistance; if R₁ is variable and is adjusted it until V_bridge = 0 the value of R₄ can then be found from the above equation.
If all four resistor values (R₁ to R₄) and the supply voltage (V) are known the voltage across the bridge (V_bridge) can be found by working out the voltage from each potential divider and subtracting one from the other. The equation for this is:

V_bridge = (R₄ / (R₃ + R₄) * V) - (R₂ / (R₁ + R₂) * V)

This can be simplified to:

V_bridge = ((R₄ / (R₃ + R₄)) - (R₂ / (R₁ + R₂))) * V

If the bridge is balanced the equivalent resistance of the circuit between V and GND is:



R₁ + R₂ in parallel with R₃ + R₄
R_E = ((R₁ + R₂) * (R₃ + R₄)) / (R₁ + R₂ + R₃ + R₄)