Question

If I=V/R and V=250 volts and R=50ohms,find the change in I resulting from an increase of 2 volts in v and an increase of 0.5ohm in R. Using total differential method.

Answer 1

The total differential for I is

$dI=\frac{1}{R}dV-\frac{V}{R^2}dR$

Approximations: given small values for $\Delta V$ and $\Delta R$ :

$\Delta I=\frac{1}{R}\Delta V-\frac{V}{R^2}\Delta R=\frac{2}{50}-\frac{250\cdot 0.5}{50^2}=-0.01$

Answer: $\Delta I=-0.01$ A.