# Question #28493

Feb 24, 2017

(a) $- 1. \overline{81}$
(b) $- 2$
(c) $- 0. \overline{8}$

#### Explanation:

(a) Given $V = I R$
For $R = 1 ,$ $I = \frac{2}{1} = 2 A$
For $R = 1.1 ,$ $I = \frac{2}{1.1} = 1. \overline{81} A$
$\therefore$ the average rate of change of $I$ with respect to $R$ in the interval of interest is$= \frac{2 - 1. \overline{81}}{1 - 1.1} = - 1. \overline{81}$

(b) $I = \frac{V}{R}$
$\implies I = \frac{2}{R}$
To find rate of change we differentiate function $I$ with respect to Resistance $R$.
$\frac{\mathrm{dI}}{\mathrm{dR}} = 2 \times \left(- 1\right) {R}^{-} 2$
$\implies \frac{\mathrm{dI}}{\mathrm{dR}} = - 2 {R}^{-} 2$
ROC at $R = 1 \Omega$
$\frac{\mathrm{dI}}{\mathrm{dR}} {|}_{1} = - 2 \times {\left(1\right)}^{-} 2$
$\implies \frac{\mathrm{dI}}{\mathrm{dR}} = - 2$

(c) $R = \frac{V}{I}$
$\implies R = \frac{2}{I}$
To find rate of change we differentiate function $R$ with respect to Current $I$
$\implies \frac{\mathrm{dR}}{\mathrm{dI}} = - 2 {I}^{-} 2$
ROC at $I = 1.5 A$
$\frac{\mathrm{dR}}{\mathrm{dI}} {|}_{1.5} = - 2 \times {\left(1.5\right)}^{-} 2$
$\frac{\mathrm{dR}}{\mathrm{dI}} = - 0. \overline{8}$