Question

A resistor is made out of a long wire having a length L. Each end of the wire is attached to a termina of a battery providing a constant voltage V0. A currect I flows through the wire. If the wire were cut in half, making two wires of length L/2, and both wires were attached to the battery (the end of both wires attached to one terminal, and the other ends attached to the other terminal), what would be the total currect flowing through the two wires?A) 4I B) 2I C) I D) I/2 E) I/4What equation do I use? What is the logic behind the equation? What is the answer?

Answer 1

Answer:

B) 2I

Explanation:

The equation that relates voltage, current and resistance is V=RI.

The equation for the resistance of a material in terms of its resistivity, length and cross-sectional area is $R=\frac{\rho L}{A}$

In this case, the length is divided by 2 while keeping its resistivity (since it's the same material) and area, which means the resistance gets divided by 2. Then, looking at the equation I=V/R and keeping V constant, one deduces that since the resistance now is half than before then current now must be twice as before.

This is all intuitive in fact, cuting a homogeneous resistor in half and leaving the rest of the variables constant makes twice as easy for the electrons to cross the conductor, thus twice the current (one has to know that all the variables involved behave linearly, as the equations show).