You are given a copper bar of dimensions 3 cm × 5 cm × 8 cm and asked to attach leads to it in order to make a resistor.(a) If you want to achieve the SMALLEST possible resistance, you should attach the leads to the opposite faces that measure

For the smallest possible resistance we should attach the leads to the opposite faces that measure 8 cm x 5 cm

Explanation:

In order to minimize resistance, we would need to have the smallest possible length of the bar and the maximum possible area for the current to pass through.

Let's first find the length and area for the following scenarios:

(a) face = 3 * 8 = 24 cm^2               ,           Length = 5 cm

(b) face = 3 * 5 = 15 cm^2               ,            Length = 8 cm

(c) face = 8 * 5 = 40 cm^2               ,           Length = 3 cm

The formula for resistance is as follows:

Resistance = Resistivity * Length / Area

Expressing this equation in terms of the above scenarios we get:

(a) Resistance = Resistivity * 5 / 24

(b) Resistance = Resistivity * 8 / 15

(c) Resistance = Resistivity * 3 / 40

We can see that scenario (c) gives us the minimum resistance as it has the smallest length to area ratio.

Thus, for the smallest possible resistance we should attach the leads to the opposite faces that measure 8 cm x 5 cm