A student constructs a battery using a potato, a strip of copper and a strip of magnesium - Scottish Highers Physics - Question 11 - 2018

To determine the internal resistance, we can analyze the provided graph showing the relationship between current (I) and terminal potential difference (V).

First, find the gradient of the graph:

$ext{gradient} = \frac{(290 \times 10^{-3}) - (470 \times 10^{-3})}{(105 \times 10^{-6}) - (55 \times 10^{-6})} = -3600 \, \Omega$

Using the formula for internal resistance:

$E = V + Ir$

Substituting values:

$E = 670 \times 10^{-3} + (400 \times 10^{-3} \cdot 75 \times 10^{-10})$

This yields:

$r = 3600 \Omega$

Electrons in the conduction band of semiconductors require sufficient energy to transition from the conduction band to the valence band. The blue LED, having a larger band gap compared to the red LED, necessitates a higher energy input to enable this transition. Since the potato battery does not supply enough potential (voltage) to provide this required energy, the blue LED does not illuminate whereas the red LED functions with the available battery output.