If-I-V-R-and-V-250-volts-and-R-50-ohms-Find-the-change-in-I-resulting-from-an-increase-of-1-volt-in-V-and-increase-of-0-5-ohm-in-R-

Question Number 130992 by benjo_mathlover last updated on 31/Jan/21

If I = \frac{V}{R} and V = 250 volts and R = 50 ohms

Find the change in I resulting from an

increase of 1 volt in V and increase of 0.5 ohm

in R .

Answered by EDWIN88 last updated on 31/Jan/21

I = f (V, R); ∴ δ I = \frac{\partial I}{\partial V} δ V + \frac{\partial I}{\partial R} δ R

\frac{\partial I}{\partial V} = \frac{1}{R}; \frac{\partial I}{\partial R} = - \frac{V}{R^{2}}

∴ δ I = \frac{1}{R} δ V - \frac{V}{R^{2}} δ R

s o w h e n R = 50; V = 250; δ V = 1 a n d

δ R = 0.5 \Rightarrow δ I = \frac{1}{50} . (1) - \frac{250}{2500} . (0.5)

δ I = \frac{1}{50} - \frac{1}{20} = - 0.03

i . e I d e c r e a s e s b y 0.03 a m p e r e s .

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