+452 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?
+15054 If I cut the wire in half and pass $175$ volts through it, how many milliamps of current will I measure?
\(R_{wire}=\dfrac{U}{I}=\dfrac{500V}{25mA}\ \ (Ohm's\ law)\\ R_{\frac{1}{2}wire}=\dfrac{1}{2}\cdot \dfrac{500V}{25mA}\\ \dfrac {I\cdot R}{U}=1\ \to \ \dfrac{A\cdot \Omega}{V}=1\\ R_{2( \frac{1}{2}wire)}=\dfrac{1}{2}\cdot \dfrac{1}{2} \cdot \dfrac{500V}{25mA}\cdot\dfrac{1000mA}{A} \cdot \dfrac{A\cdot \Omega}{V}=5000\Omega\)
\(I=\dfrac{U}{R_{2( \frac{1}{2}wire)}} =\dfrac{175V}{5000\Omega}\cdot \dfrac{1000mA}{A}\cdot \dfrac{A\cdot \Omega }{V}=\color{ blue}35mA \)
35 milliamps of current will I measure.
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