Calculating Resistance In Circuit

[Andy111]

Homework Statement

A loop circuit has a resistance of R and a current of 1.8A. The current is reduced to 1.3A when an additional 2.7 ohm resistor is added in series with R.

What is the value of R?

Homework Equations

I is constant throughout a series circuit
V is shared in a series
Total resistance=the sum of the resistors in series

V=I x R

The Attempt at a Solution

I substituted R (in the equation V=IR) with 4.7+R because this would represent the total resistance in the series. I knew that I was 1.3A. I calculated the Voltage on the 4.7 resistor (using V=IR) and got 6V. So then I substitued V total with 6 + V.

I ended up with the following equation. 6+V=1.3(4.7+R). I then tried substituting V (of the unknown resistor) with 1.3R, but then I realized that couldn't possibly work, because the R's would cancel. Then I tried 1.8R instead so I would end up with the equation .5R=.11, R=.22 but that doesn't sound right.

 

[Snazzy]

You don't have to figure out V. In the first case, you have $$\frac{V}{R}=1.8$$

And in the second case, you have $$\frac{V}{2.7+R}=1.3$$

Two unknowns and two equations.

 

[Andy111]

Okay. I got an answer of 7.02 using those equations, but it was incorrect.

 

[Andy111]

Nevermind, I see where the mistake was. I used 2.7, it's supposed to be 4.7