Series and parallel electrical circuits are two basic ways of wiring components. series and parallel circuits The naming describes the method of attaching components, i.e. one after the other, or next to each other. characteristics of series and parallel circuits As a demonstration, consider a very simple circuit consisting of two lightbulbs and one 9V battery. If a wire joins the battery to one bulb, to the next bulb, then back to the battery, in one continuous loop, the bulbs are said to be in series. If, on the other hand, each bulb is wired separately to the battery in two loops, the bulbs are said to be in parallel.
The measurable quantities used here are R, resistance, measured in ohms (Ω), I, current, measured in amperes (A) (coulombs per second), and V, voltage, measured in volts (V) (joules per coulomb).
Series circuits
Series circuits are sometimes called cascade-coupled or daisy chain-coupled.
The same current has to pass through all the components in the series. An ammeter placed anywhere in the circuit would indicate the same current.
Resistors
To find the total resistance of all the components, add together the individual resistances of each component:
- for components in series, having resistances R1, R2, etc.
To find the examples of series and parallel circuits current, I, use Ohm's law.
- I = V / Rtotal
To find the voltage across any particular component with resistance Ri, use Ohm's law again.
-
- Where I is the current, as calculated above.
Note that the components divide the voltage according to their resistances, so, in the case of two resistors:
- V1 / V2 = R1 / R2
Inductors
Inductors combined series and parallel circuits 5th grade science series and parallel circuits follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if you have two inductors in series, there are two possible equivalent inductances:
- Ltotal = (L1 + M) + (L2 + M) or
- Ltotal = (L1 − M) + (L2 − M)
Which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
When there are more than two inductors, it gets more complicated, since you have to take into account the mutual inductance of each of them and how each coils influences the other.
So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:
Parallel circuits
The voltage is the same across all the components in parallel.
To find the total current, I, use Ohm's Law on each loop, then sum. (See Kirchhoff's circuit laws for an explanation parallel and series circuits of why this works). Factoring out the voltage (which, again, is the same across all components) gives:
Resistors
To find the total resistance of all the components, add together the individual reciprocal of each resistance of each component, and take the reciprocal of the sum:
- for components in parallel, having resistances R1, R2, etc.
The above rule can be calculated by using Ohm's law for the whole circuit
- Rtotal = V / Itotal
and substituting for Itotal
To find the current in any particular component with resistance Ri, use Ohm's law again.
- Ii = V / Ri
Note, that the components divide the current according to their reciprocal resistances, difference between series and parallel circuits so, in the case of two resistors:
- I1 / I2 = R2 / R1
Inductors
Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
Once again, if the inductors are situated in each others' magnetic fields, one has to take into account mutual inductance. If the mutual inductance between two coils in parallel is M then the equivalent inductor is:
- or
And once again, which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
The principle is the same for more than two inductors, but you now have to take into account the mutual inductance of each inductor on each other simple series and parallel circuits inductor and how they influence each other. So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:
Notation
The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,
See also
- Y-Δ transform (a.k.a. Star-Triangle transformation)
Electronics Topics
The field of electronics is the study and use of systems that operate by controlling the flow of electrons or other electrically charged particles in devices such as thermionic valves and semiconductors. The design and construction of electronic circuits to solve practical problems is part of the fields of electronic engineering, and the hardware design side of computer engineering. The study of new semiconductor devices and their technology is sometimes considered as a branch of physics.
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Em - F | E - El | G - H | I - K | L - Ma
