In a single arm strain gauge bridge for force measurement on a brass member, the circuitry is 5m away maintained in a temperature controlled enclosure and connected by copper leads with the gages. The bridge and amplifier together has an overall sensitivity of 10-5 V/N. The resistance of the gauge is 100 and the gauge current which may approximately be measured constant is 25mA. Calculate the limits of error induced by ambient temperature variation in the sensor and the leads in the range 0-50C. the following specification of the strain gauge are given Tempco of gauge factor : +0.75% 100F Tempco of gauge resistance : Matches the member on which the gauge is bonded for zero temperature induced strain Tempco of copper : 43  10-4 / C Tempco of brass : 20  10-4 / C Young’s modulas of brass : 2  1011 N / m2 Resistance of lead : 2m / ohm

The error induced by ambient temperature variation in the sensor and the leads can be calculated by considering the temperature coefficients of the materials involved and the range of temperature variation.

1. Calculate the change in resistance of the strain gauge due to temperature variation:

The Tempco of the gauge resistance matches the member on which the gauge is bonded, which is brass. Therefore, the change in resistance of the gauge (ΔRg) due to temperature variation from 0 to 50°C is:

ΔRg = Rg * Tempco_brass * ΔT = 100Ω * 20 * 10^-4/°C * 50°C = 1Ω

2. Calculate the change in resistance of the copper leads due to temperature variation:

The resistance of the leads is given as 2m/ohm, which means the resistance per meter is 0.5 ohm/m. Since the leads are 5m long, the total resistance of the leads (Rl) is 2.5Ω. The change in resistance of the leads (ΔRl) due to temperature variation from 0 to 50°C is:

ΔRl = Rl * Tempco_copper * ΔT = 2.5Ω * 43 * 10^-4/°C * 50°C = 0.5375Ω

3. Calculate the total change in resistance due to temperature variation:

The total change in resistance (ΔR) is the sum of the changes in the gauge and the leads:

ΔR = ΔRg + ΔRl = 1Ω + 0.5375Ω = 1.5375Ω

4. Calculate the error in force measurement due to the change in resistance:

The sensitivity of the bridge and amplifier is given as 10^-5 V/N. Therefore, the error in force measurement (ΔF) due to the change in resistance is:

ΔF = ΔR / Sensitivity = 1.5375Ω / 10^-5 V/N = 153750N

Therefore, the limits of error induced by ambient temperature variation in the sensor and the leads in the range 0-50°C is ±153750N.