+1911 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 = 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?
0 \(R=\frac{\rho l}{A}\) If \(l\) becomes \(l/2\) and everything else is the same then:
\(R_0=R/2\)
\(V=IR\\ R=\frac{V}{I}\\ R=\frac{500}{0.025}=20000\Omega\)
\(R_0=10000\Omega\)
So:
\(V_0=I_0R_0\\ I_0=\frac{V_0}{R_0}=\frac{175}{10000}\\ \boxed{I_0=17.5\text{ milliamps}}\)
