How to Calculate Series Circuits

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Series circuits are a useful starting-off point for understanding more complex circuits. Even the mere introduction of an alternating current source can introduce students to concepts that are fundamental to far more complex circuits. One important concept for calculating series circuits is equivalency. For example, a series of resistors can have the same effect on the circuit's current as a single, equivalent resistor. Once you determine the resistance of the equivalent resistor, you can solve for the current of the circuit. This approach works for inductors and capacitors as well.

  • Calculate the current of a series circuit with no inductors or capacitors by dividing the electromotive force (emf) of the voltage source by the sum of the resistors' resistances. You're therefore treating the resistors as if they are one resistor with a resistance equivalent to the sum of the series resistors' resistances. This approach applies regardless of whether the emf is constant or variable.

  • Calculate the current of a series circuit with an inductor with the formula i = emf/R (1-exp[-t/τ]). Here, τ = L/R and emf is constant. L is the inductance of the inductor. Use Leff for L as calculated in Step 4 below if there are more than one inductors. Here, "emf" is the voltage of the power source.

  • Calculate the current in a series circuit with an alternating emf of frequency ω by first calculating the impedance, which is the square root of R^2 + (ωL - 1/ωC)^2. Here, R is the resistance of the circuit, L is the inductance of the inductor and C is the capacitance of the capacitor. Denote the impedance with a "Z." Then the maximum value of the current is 1/Z times the maximum value of the emf.

  • Calculate the effective inductance, Leff, of several inductors in series by merely summing their inductances: Leff = L1 + L2 +... Use Leff in place of L in the previous steps.

  • Calculate the effective capacitance, Ceff, of several capacitors in series by summing their reciprocals, and then taking the reciprocal of that sum. In other words, Ceff obeys the formula 1/Ceff = 1/C1 + 1/C2 +... For capacitors C1, C2, etc., use Ceff in place of C in the above equations.

References

  • Photo Credit circuit board image by Gale Distler from Fotolia.com
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