This model can be used to determine the null conditions of a Wheatstone bridge or to determine the out-of-null output voltage as a function of arm resistance. Resistors R1 ... R4 are the four arms of the bridge and RL represents the input resistance of the detector or null voltage read-out device. This model requires an iterative solution; the "guess" variable can be the voltage or current in any one of the arms. In the example variable sheet shown below, an off-null sensitivity of 24.8 mV per ohm is demonstrated for a nearly balanced 100 ohm bridge with an excitation voltage of 10 volts and RL=100K.
Variable Sheet _________________________________________________________________________________ St Input Name Output Unit Comment E1 4.9751369 volts Voltage across R1 (volts, mV, �V) I1 .04975137 Amps Current through R1 (Amps, mA, �A) 100 R1 Ohms Resistance of arm 1 (Ohms, Kohms, MOhms) E2 4.9999876 volts Voltage across R2 (volts, mV, �V) I2 .04999988 Amps Current through R2 (Amps, mA, �A) 100 R2 Ohms Resistance of arm 2 (Ohms, Kohms, MOhms) E3 5.0248631 volts Voltage across R3 (volts, mV, �V) I3 .04975112 Amps Current through R3 (Amps, mA, �A) 101 R3 Ohms Resistance of arm 3 (Ohms, Kohms, MOhms) E4 5.0000124 volts Voltage across R4 (volts, mV, �V) I4 .05000012 Amps Current through R4 (Amps, mA, �A) 100 R4 Ohms Resistance of arm 4 (Ohms, Kohms, MOhms) EL 24.85071 mV Voltage across RL (volts, mV, �V) IL 2.4851E-7 Amps Current through RL (Amps, mA, �A) 100000 RL Ohms Resistance of detector (Ohms, Kohms, MOh 10 Vb volts Excitation voltage (volts, mV, �V) Rule Sheet _________________________________________________________________________________ S Rule * E1=I1*R1 "Ohms Law for R1 * E2=I2*R2 "Ohms Law for R2 * E3=I3*R3 "Ohms Law for R3 * E4=I4*R4 "Ohms Law for R4 * EL=IL*RL "Ohms Law for RL * E1+E3=Vb "Kirchoffs Law for voltage * E2+E4=Vb "Kirchoffs Law for voltage * I1=I3+IL "Kirchoffs Law for current * I2=I4-IL "Kirchoffs Law for current * EL=E3-E4 "Kirchoffs Law for voltage