# Physicopoeia

###### φυσικοποιΐα

# CALCULATING RESISTANCE VALUES FROM GRAPHS

It's not unknown for some sources to say that you can find the resistance of a resistor by calculating the gradient of its *V*-*I* graph. As long as the resistor is obeying Ohm's Law, this is (coincidentally) correct. However, the definition of *R* is *V* ÷ *I*, not the rate of change of *V* with *I*.

However, a worse misunderstanding can occur if you are then asked to find the resistance of (say) a filament bulb at a given pd from its (curved) *V*-*I* graph. Since *V* isn't proportional to *I* for a bulb, the gradient idea might lead you to think that you should take the gradient of a tangent to the *V*-*I* curve, like you would to find the instantaneous velocity of an accelerating object from its distance-time graph. In fact, since *R* = *V* ÷ *I* by definition, you just read off the values of *V* and *I* at the required point and divide one by the other: no need for tangents at all.

A similar issue exists when it comes to finding Young's modulus values from stress-strain graphs.