Problem — V-I characteristic

Problem

The experimental values of the voltage–current characteristic of an unknown component are:

$V$ (V)	1,0	2,0	3,0	4,0
$I$ (mA)	2,5	5,0	7,5	10,0

(a) Does the component follow Ohm’s law? (b) Determine its resistance.

Solution

(a) Is it ohmic? — a component follows Ohm’s law if the ratio $V/I$ is constant, i.e. if the characteristic is a straight line through the origin. Let us calculate $V/I$ for each point: $\frac{1{,}0}{2{,}5\cdot 10^{-3}} = 400, \quad \frac{2{,}0}{5{,}0\cdot 10^{-3}} = 400, \quad \frac{3{,}0}{7{,}5\cdot 10^{-3}} = 400, \quad \frac{4{,}0}{10{,}0\cdot 10^{-3}} = 400\ \ (\Omega)$

The ratio is constant: doubling the voltage doubles the current. The component follows Ohm’s law (it is ohmic).

(b) Resistance — it is the inverse slope of the characteristic, i.e. the common value found above: $R = \frac{V}{I} = \frac{4{,}0\ \text{V}}{10{,}0\cdot 10^{-3}\ \text{A}} = 400\ \Omega$

$\ev{\text{(a) yes, ohmic}; \quad \text{(b) } R = 400\ \Omega}$

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Topics: Circuiti elettrici Concepts: Legge di Ohm Skills: Lettura dei grafici