Given voltage, solve for unknown resistor in a circuit

  • #1

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?
 

Answers and Replies

  • #2
gneill
Mentor
20,913
2,862
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 :)
 
  • #3
Thanks! I guess I shouldn't be so lazy. ha
 

Related Threads on Given voltage, solve for unknown resistor in a circuit

Replies
2
Views
4K
Replies
3
Views
2K
Replies
3
Views
2K
Replies
6
Views
3K
Replies
9
Views
836
Replies
4
Views
6K
Replies
4
Views
12K
Replies
21
Views
1K
Replies
3
Views
5K
Replies
9
Views
3K
Top