Question
D) A strain gauge has two active gauges subject to equal and opposite strains (tension and compression). The zero-strain resistances of the gauges are 110Omega Two dummy gauges are used to complete the four arm circuit. The power supply is 10.2V The galvanometer resistance is 50Omega and reads 50mu A Assume a gauge factor of 2.32. Determine the strain.
Solution
4.7
(254 Votos)
Alana
Especialista · Tutor por 3 anos
Resposta
To determine the strain, we can use the following formula:Strain = (Change in Resistance / Original Resistance) * Gauge FactorFirst, let's calculate the change in resistance for the active gauges. Since the zero-strain resistances of the gauges are 110Ω, the change in resistance can be calculated as:Change in Resistance = 2 * (Gauge Factor * Strain * Original Resistance)Now, we can rearrange the formula to solve for the strain:Strain = (Change in Resistance / (2 * Gauge Factor * Original Resistance))Given that the power supply is 10.2V, the galvanometer resistance is 50Ω, and the galvanometer reads 50μA, we can calculate the change in voltage across the active gauges:Change in Voltage = (Power Supply * (Change in Resistance / (2 * Original Resistance))) / (1 + (Change in Resistance / (2 * Original Resistance)))Now, we can substitute the values into the formula to calculate the strain:Strain = (Change in Voltage / (Power Supply * (Galvanometer Resistance / (Galvanometer Resistance + Change in Resistance / (2 * Original Resistance)))) * Gauge FactorSubstituting the given values:Strain = (10.2 * (50 / (50 + (Change in Resistance / (2 * 110)))) * 2.32Now, we need to solve for the change in resistance. We can use the fact that the galvanometer reads 50μA:Change in Resistance = (Galvanometer Resistance * Galvanometer Current) / (1 + (Galvanometer Resistance / (Galvanometer Resistance + Change in Resistance / (2 * Original Resistance))))Substituting the given values:Change in Resistance = (50 * 50μA) / (1 + (50 / (50 + Change in Resistance / (2 * 110))))Now, we can solve for the change in resistance:Change in Resistance ≈ 0.0005ΩFinally, we can substitute the change in resistance back into the strain formula:Strain = (10.2 * (50 / (50 + (0.0005 / (2 * 110)))) * 2.32Strain ≈ 0.000232 or 0.0232%Therefore, the strain is approximately 0.0232%.