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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?

 Feb 20, 2024
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\(R=\frac{\rho l}{A}\) 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:

\(V_0=I_0R_0\\ I_0=\frac{V_0}{R_0}=\frac{175}{10000}\\ \boxed{I_0=17.5\text{ milliamps}}\)

 Feb 20, 2024

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