Wire A has the same length and twice the radius of wire B. Both wires are made of the same material and carry the same current. Which of the following equations is true concerning the drift velocities vA and vB of electrons in the wires?

vA = vB/4

vA = vB/2

vA = 4vB

vA = vB

vA = 2vB

The answer is vA = 4vB

Explanation:

The drift velocity of an electron in a wire is inversely proportional to the resistance in the wire. Therefore, the higher the amount of resistance in the wire, the lower the value of velocity.

To find the answer, we need to figure out how the resistance in each wire would differ with each other on the basis of the given paranater.

We know that the length is the same, the current is the same, and the metal type is the same as well. The difference is the area. Now, resistance is inversely proportional to the area of the wire's cross section which means that a larger cross sectional area would indicate a lower resistance.

Now, wire A has twice the radius of wire B. This means that the cross sectional area of wire A is 4 times larger than the area of wire B (using a simple formular of Pi x R squared). Therefore the resistance of wire A is a quarter of the resistance in wire B.

We can see that due to this, the velocity in wire A would be 4 times the velocity in wire B.