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Series and parallel circuits
In electrical circuits series and parallel are two basic ways of wiring components. The naming comes after the method of attaching components, i.e. one after the other, or next to each other. 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.
Series circuits are sometimes called cascade-coupled or daisy chain-coupled.
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 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
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 of why this works). Factoring out the voltage (which, again, is the same across all components) gives:
- 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, so, in the case of two resistors:
- I1 / I2 = R2 / R1
The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,
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