Resistance in a Series Circuit

Resistance in a Series Circuit

This Formula Solver! Series program shows the step-by-step solution for finding resistance in a series circuit (using up to four resistance values which you can enter yourself).

Resistance in a Series Circuit

Dear Professor Cram:

I have a question about series circuits. There are 3 resistors, R1 is 10kohms/.5W and R2 is 3.3kohms/.250W and the third is unknown. If the circuit draws a current of 1.5mA from a 27V source, how do i calculate the ohmic value of the third resistor?

Nicholas, Mohawk College

Thank you for your question, Nicholas. Physics is not normally my forte, but I can help you with this one.

Our first step is to determine the power and resistance for the circuit as a whole. We are given the power in volts and current in milliamps, so to find the power we should convert milliamps to amps:

  • 1.5mA x 1A/1000mA = 0.0015A

With the current now expressed in Amps, we can calculate the power for this circuit:

  • power = current x volts, or
  • power = 0.0015A x 27V, or
  • power = 0.0405W

Now let's find the total resistance in the series circuit by using Ohm's law:

  • resistance = volts/current, or
  • resistance = 27V/0.0015A, or
  • resistance = 18,000 ohms or 18kohms

Now comes the fun part. The resistance values given in the question are not the resistance in this circuit but resistance ratings based on wattage, as evidenced by the ohms/W units. To find their resistance in this circuit, we'll need to convert these values to ohms/0.0405W as our next step:

  • r1/0.0405W = 10000ohms/.5W
  • r1 = (10,000ohms)(.0405W)/(.5W), or 810 ohms
  • r2/0.0405W = 3300ohms/.25W
  • r2 = (3,300ohms)(.0405W)/(.25W), or 534.6 ohms

Now for the big finish. We know the total resistance of the series circuit (18,000 ohms). We know the resistance of two of the three resistors. We know that in a series circuit, the total resistance is the sum of all the resistors in series. Thus, the third resistor is:

  • r3 = 18,000 ohms – (810 ohms + 534.6 ohms), or
  • r3 = 16,655.4 ohms

I hope this helps. Let us know if you need anything else.

Good studying,

Professor Cram