Given voltage, solve for unknown resistor in a circuit

[acdurbin953]

Homework Statement

An ohmic resistor (R1 = 3.5 kΩ) and circuit element X are connected in series to a battery of unknown voltage V0. Circuit element X is of unknown resistance. It is observed that the absolute value of the voltage across resistor R1 is 5.0 V.
The battery voltage is measured and found to be equal to 8.0 V.
The resistance of X must be what?

Homework Equations

V=IR
Found the current to be 0.0014 amps by doing 5.0 V/3500 kΩ

The Attempt at a Solution

My trouble is that I have worked the problem, but have come up with 2 similar solutions that seem plausible.

Solution 1: 8V = 0.0014(R₁+R₂), solving for R₂ gives 2.21kΩ
Solution 2: Since the total voltage is 8 and R₁ is 5, R₂ must be 3. So then 3V = 0.0014(R₂₎, and solving for R₂ gives 2.14kΩ.

Both attempts are so close together that I have no idea which is right! Are they both more or less correct and one is just more accurate than the other?

 

[gneill]

Both methods will give you the correct (same) answer if you pay attention to rounding and truncation issues.

Don't round intermediate values for calculation. Carry sufficient digits to ensure that rounding and truncation errors do not creep into your valid significant digits. Scientific notation can go a long way to help avoid tired calculator fingers from entering all those leading zeros :)

 

[acdurbin953]

Thanks! I guess I shouldn't be so lazy. ha