Question

Independent voltage measurements \((\mu \pm \sigma)\) of three sensors where \(\mu\) and \(\sigma\) are the mean and standard deviation of the measurements, respectively are as follows: \(v_1 = 4.52 \pm 0.02 \, \text{V}, \, v_2 = 4.21 \pm 0.20 \, \text{V}, \, v_3 = 3.96 \pm 0.15 \, \text{V}\). The measurement uncertainty in \(v_1 + v_2 + v_3\) is ________ V (rounded off to two decimal places).

Hint:

For the uncertainty in the sum of independent measurements, add the squares of the uncertainties and take the square root.

Answer 1

Correct Answer: 0.25

The measurement uncertainty in the sum of independent variables is given by: \[ \sigma_{v_1 + v_2 + v_3} = \sqrt{\sigma_1^2 + \sigma_2^2 + \sigma_3^2} \] Substitute the given uncertainties: \[ \sigma_{v_1 + v_2 + v_3} = \sqrt{(0.02)^2 + (0.20)^2 + (0.15)^2} \] \[ \sigma_{v_1 + v_2 + v_3} = \sqrt{0.0004 + 0.04 + 0.0225} = \sqrt{0.0629} \] \[ \sigma_{v_1 + v_2 + v_3} \approx 0.25\ \text{V} \] Thus, the measurement uncertainty is: \[ \boxed{0.25\ \text{to}\ 0.26\ \text{V}} \] Final Answer: 0.25–0.26 V