+448 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?
+15001 I = V/R
\(R_1=\frac{V_1}{I_1}=\frac{500V}{0.025A}=\color{blue}20k\Omega\)
I halve the length of the wire, hence the resistance \(R_1\).
\(I_2=\frac{V_2}{R_2}=\frac{175V}{10k\Omega}=\color{blue}17.5mA\)
I apply the voltage\(V_2\) to both halves of the wire, thus halving the resistance \(R_1\).
\(I_3=\frac{V_2}{R_3}=\frac{175V}{5k\Omega}=\color{blue}35mA\) in both wire halves together.
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