Electric Potential — Question 6

Question 6

Hard measurement bounds propagate through charge times voltage

Independent hard bounds are $V_A=10.0\pm.5$ V, $V_B=35.0\pm1.0$ V, and $q=2.00\pm.10$ nC. The plus-minus values specify allowed intervals, not standard deviations.

1. Find the full allowed interval for $V_B-V_A$.

2. Find the nominal energy change and its exact worst-case interval.

Question 6 - Solution

Hard measurement bounds propagate through charge times voltage

(a) Method and calculation

$$\Delta V_{\min}=34.0-10.5=23.5\,\mathrm V.$$$$\Delta V_{\max}=36.0-9.5=26.5\,\mathrm V.$$

(b) Interpretation and further calculation

$$\Delta U_{\mathrm{nominal}}=(2.00\,\mathrm{nC})(25.0\,\mathrm V)=50.0\,\mathrm{nJ}.$$$$\Delta U\in[(1.90)(23.5),(2.10)(26.5)]\,\mathrm{nJ}=[44.65,55.65]\,\mathrm{nJ}.$$

Physical check

All factors are positive over their intervals, so endpoint multiplication gives the exact extrema without statistical assumptions.