Question

A company makes two electronic circuit boards that require the same resistance. The Pro-X board runs on 120 volts, while the Pro-I board runs on 90 volts. If the current running through the Pro-I board is 15 fewer milliamps (mA) than the current running through the Pro-X board, how much current is running through each board? Which of the following rational equations bests models this situation?

Answer 1

60 mA and 45 mA

`\displaystyle (120)/(R)=(90)/(R)+0.015`

Explanation:

Application of Linear Equations

The voltage V measured in a resistive element of an electrical circuit or resistance R is

`V=I.R`

Where I is the current flowing through the resistor. Solving for I

`\displaystyle I=(V)/(R)`

There are two electronic circuit boards that have the same resistance. The Pro-X board runs on 120 volts and the Pro-I board runs on 90 Volts. We know that the current running through this last one is 15 mA fewer than the current through the Pro-X board. It means

`\displaystyle (120)/(R)=(90)/(R)+0.015`

Rearranging:

`\displaystyle (120)/(R)-(90)/(R)=0.015`

Operating

`\displaystyle (30)/(R)=0.015`

Or, equivalently

`\displaystyle R=(30)/(0.015)=2000\Omega`

Thus, the current through the Pro-X board is

`\displaystyle (120)/(2000)=60\ mA`

And the current through the Pro-I board is

`\displaystyle (90)/(2000)=45\ mA`