Understanding Electrical Circuits: Series, Parallel, and Power
Equivalent Circuit
To perform the electrical calculations of a circuit with several resistors, we calculate the value of a single resistor, equivalent to the association of the resistors in the circuit. The circuit formed with the equivalent resistors is called an equivalent circuit. We can obtain three things from this circuit:
- The currents flowing through the circuit
- The potential drops across the components
- The dissipated power and the delivered power
Series Circuit
In a series circuit (Figure 1), the resistors are connected one after the other, so all of the electrical current flows through all of the load devices. There is only one possible path for the current to flow through. The calculation of electrical variables is summarized in the table below, where Rt, It, and Vt refer to the variables of the equivalent circuit.
Series-Parallel Combination Circuits
In series-parallel combination circuits (Figure 3), there are elements in series and elements in parallel. To solve a series-parallel combination circuit, we need to find out which resistors are in series and which are in parallel. Then we can apply the equations for each case (we will see this in the example exercise below).
Relationship Between Delivered Power and Consumed Power
In the circuits we have seen, did you notice that the power delivered by the power source must be equal to the sum of the power dissipated by each resistor? This is true for any circuit, whether in series, parallel, or combination.
Power delivered = power consumed
Association of Power Sources
So far, the circuits we have seen had only one voltage source. We will now see how to solve circuits with more than one power source. Like resistors, power sources can be associated in series or parallel.
Associating Power Sources in Series
Power sources are associated in series when they are on the same branch of a circuit. Power sources in series can be replaced by a single equivalent source. We must calculate the value of this source by adding the values of the separate power sources.
Vt = V1 ± V2 ± ….. ± Vn
Remember: if the positive terminal of a power source is connected to the negative terminal of the next one, the voltages of the power sources are added together. If the positive terminal of the power source is connected to the positive terminal of the next one, the voltages are subtracted.
Associating Power Sources in Parallel
In parallel, we can only connect power sources that are equal. We do this by connecting the terminals of the same sign. In this case, the equivalent voltage is the same for each; the only effect is that we increase the time that the circuit can operate for.
Resistors
Resistors limit the flow of electrical current through a circuit. A resistor usually has four colored bands; the last of these is generally gold or silver.
We interpret the color code like this. For a resistor with the colors orange – red – red – gold:
- 1st band: orange = 3
- 2nd band: red = 2
- 3rd band: red, multiplier = x 100
- So the value is: 32 x 100 = 3,200 Ω = 3k2
- 4th band: gold
So the tolerance is ±5%
In other words, the value of the resistor is 3,200 Ω + 160 Ω (which is the margin of error offered by the manufacturer.
Variable Resistors or Potentiometers
When we need to adjust the value of the resistance in a circuit, we use variable resistors or potentiometers. We can change the resistance value of these components from 0 to their maximum value by moving the wiper.
For example, in the resistor in the figure, if we connect the terminals:
- Between A and B → Rt = 220 Ω
- Between A and C → R1 = 156 Ω
- Between C and B → R2 = 79 Ω