Physicopoeia

φυσικοποιΐα
THINGS I WISH I'D KNOWN WHEN I STARTED TEACHING PHYSICS

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.