How Do You Compare Resistance in a Carbon Resistor and an LED Using a V-I Graph?

[P1nkButt3rflys]

A) The graph shows V-I curves for two conductors. One is measured for a carbon resistor and obeys Ohm's law; the other is for a light-emitting diode (LED) and shows non-ohmic behaviour. What is the resistance of the carbon resistor?

B) For what value of current is the resistance of the LED the same as that of the carbon resistor? (Use a ruler and a triangle to draw on the diagram.)

I got the first portion. The carbon resistor is the linear line and the LED is the curved line. Using the graph I found R = 10 ohm for A. But cannot figure out how to solve B, any suggestions?

 

[jackarms]

For the LED, you can find the resistance at a particular value of current and voltage with the equation $R = \frac{V}{I}$ (note that this isn't the same as Ohm's Law -- it can only be used to find the the instantaneous resistance, and does not describe the resistance of the conductor at all values of the voltage).

Graphically, $\frac{V}{I}$ is the slope of the graph, which you can find with tangent lines.

 

[NascentOxygen]

The slope of the curve defines its resistance at that region of operation. So draw tangents everywhere, to see how the slope changes.

For the carbon resistor, the tangents everywhere are the same, its resistance does not vary.

 

[rude man]

The prblem in (b) should have asked specifically for dynamic resistance. The LED "resistance" could equally well mean static resistance in which case the LED always has a larger resistance than the resistor. For example, an ohmmeter would measure static resistance = V/i at whatever the meter current i happens to be.