Wheatstone Bridge Example

The figure below shows a bridge circuit with values of the circuit elements. The battery voltage is 5V and the internal resistance is negligible. The galvanometer has a current sensitivity of 10mm/µA and an internal resistance of 100Ω. Calculate the deflection of the galvanometer caused by the 5Ω unbalance in arm BC

Solution:

Thevenin voltage:

$Thevenin Resistance \left(R_{TH}\right)$

$R_{TH} = 100 // 200 + 1000 // 2005$

$\; \; \; \; = 734 \Omega$

${\mathrm{I}}_{\mathrm{g} }= \frac{{\mathrm{V}}_{\mathrm{TH}}}{{\mathrm{R}}_{\mathrm{TH}} + {\mathrm{R}}_{\mathrm{g}}}$

$\; =\frac{2.77 \mathrm{mV}}{734\mathrm{\Omega } + 100\mathrm{\Omega }}$

$\; =3.32 \mathrm{uA}$

Galvanometer Deflection

d = 3.32 uA x 10 mm / uA

   = 33.2 mm

Application - It is extensively used in industrial applications like quality control of resistance wires, determination of resistance of transformers, motor winding, relay coils and solenoids, calibration of sensors.