Basic Electricity: Calculating Total Resistance in Complex Circuits
Introduction
This article presents a method of solving for total resistance in complex circuits containing resistors. It assumes the reader has the following knowledge:
Ohm’s Law
Series Circuits
Parallel Circuits
Algebra
Review of Ohm’s Law
Ohm’s Law states that the pressure in volts is equal to the product of the resistance in ohms and the current in amperes
Review of Series Circuits
In a series circuit:
The total voltage is the sum of the voltages across each resistor
The total resistance is the sum of the individual resistances
The current is the same throughout the circuit.
Review of Parallel Circuits
In a parallel circuit:
The voltage is the same across each branch of the circuit
The total current is the sum of the currents through each branch
The total resistance is less than the least resistance.
1/Rt = 1/R1 + 1/R2 + … + 1/Rn
Or
For a parallel circuit containing two resistors, we can use the formula
Rt = R1*R2/(R1+R2)
Solving For Total Resistance In A Complex Circuit
Look at the circuit in figure one. To solve for the total resistance, we have to simplify the circuit by finding equivalent resistances. In figure one, we can see that we have three parallel circuits that we could find equivalent resistances for. The three parallel circuits are:
R1//R2
R4//R5
R7//10
Where the symbol // means “in parallel with.”
The total resistance of R1//R2 is:
R12 = R1*R2/(R1+R2)
Likewise the total resistance of R4//R5 is:
R45 = R4*R5/(R4+R5)
And the total resistance of R7//R10 is
R71 = R7*R10/(R7+R10)
Our new circuit containing R12, R45 and R71 is shown in figure two. We see that there are three series circuits we could solve for. The three series circuits are
R12 and R3
R45 and R9
R71 and R8
Solving for total series resistance
R123 = R12 + R3
R459 = R45 + R9
R718 = R71 + R8
The new circuit containing R123, R459 and R718 is shown in figure three. We can see that R123 and R459 are in parallel. Solving for the parallel combination of R123 and R459:
R19 = R123//R459 = R123*R459/(R123+R459)
This leaves us with the circuit of figure four. The final calculation is the total resistance of the series circuit containing R19 and R718.
Rt = R19 + R718.
Hence we have calculated the total resistance. Rt is the total resistance of the circuit shown in figure one.
This concludes this article. The next article will show a second method of calculating total resistance in a complex circuit.
- By John Mario | Associated Content
- Naiomi Solomon
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