Question

A strain gage having nominal resistance of 1000 \( \Omega \) has a gage factor of 2.5. If the strain applied to the gage is 100 \( \mu \)m/m, its resistance in ohm will change to \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).

Hint:

To calculate the change in resistance for a strain gage, use the formula \( \Delta R = R_0 \times G \times \varepsilon \) where \( R_0 \) is the nominal resistance, \( G \) is the gage factor, and \( \varepsilon \) is the strain.

Answer 1

Correct Answer: 1000.25

The change in resistance due to strain can be calculated using the formula: \[ \Delta R = R_0 \times G \times \varepsilon \] where \( R_0 \) is the nominal resistance, \( G \) is the gage factor, and \( \varepsilon \) is the strain.
Given: \( R_0 = 1000 \, \Omega \), \( G = 2.5 \), and \( \varepsilon = 100 \, \mu \text{m/m} = 0.0001 \), we get: \[ \Delta R = 1000 \times 2.5 \times 0.0001 = 0.25 \, \Omega. \] The new resistance is: \[ R_{\text{new}} = R_0 + \Delta R = 1000 + 0.25 = 1000.25 \, \Omega. \] Thus, the resistance will change to \( 1000.25 \, \Omega \).