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# Algebra

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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?

Aug 5, 2024

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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.

!

Aug 6, 2024
edited by asinus  Aug 6, 2024
edited by asinus  Aug 6, 2024
edited by asinus  Aug 6, 2024