In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:

Question

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:

\[I=\frac{V}{R}.\]
It's also true that resistance is directly proportional to the length of the wire. We have a piece of wire. We pass $500$ volts through this wire and measure $25$ milliamps of current. If I cut the wire in half and pass $175$ volts through it, how many milliamps of current will I measure?

Answer 1

Since resistance is directly proportional to the length of the wire, cutting the wire in half will cut the resistance in half. This means that if we double the voltage, we should double the current. Since we pass $175$ volts through the wire (half as much as before), we should have half as much current as before. Since we originally had $25$ milliamps, we should have $\boxed{12.5}$ milliamps of current.