Power in Electric Circuits — Question 10

Question 10

A resistor power limit must hold at the worst tolerance combination

A resistor is nominally $R_0=100\,\Omega$ with hard tolerance $\pm5$ percent. Its allowed dissipation is .250 W. A DC source has nominal voltage $V_0$ and hard tolerance $\pm2$ percent.

1. Find the largest nominal voltage that respects the limit for every allowed combination.

2. Find the worst-case current at that nominal voltage and compare with using only nominal R and V.

Question 10 - Solution

A resistor power limit must hold at the worst tolerance combination

(a) Method and calculation

$$P_{\max}=\frac{(1.02V_0)^2}{.95R_0}\le.250\,\mathrm W.$$$$V_0\le\frac{\sqrt{(.250)(95)}}{1.02}=4.77784\,\mathrm V.$$

(b) Interpretation and further calculation

$$I_{\max}=\frac{1.02V_0}{95}=\sqrt{.250/95}=.0512989\,\mathrm A.$$$$V_{0,\mathrm{naive}}=\sqrt{(.250)(100)}=5.00\,\mathrm V.$$The naive choice exceeds the allowed power at high voltage and low resistance.

Physical check

Worst heating uses the smallest resistance under voltage drive; under fixed current it would use the largest resistance.