The components in an electrical circuit can be connected in many different ways. The two most frequent and simplest arrangements are called series and parallel. Circuits composed entirely of components in series or parallel are known as series circuits and parallel circuits, respectively. Although both may consist of the same components, their arrangement plays a crucial role in how current, voltage, resistance, and a variety of other electrical properties are distributed among the circuits components as well as how the overall circuit functions.
Series Circuits
In these circuits, the current passes through each component in the circuit. Therefore the current is the same through each component as there is only one path in a series circuit in which current can flow.
I=I1=I2=In
The total resistance in a series circuit is simply the sum of each component’s individual resistances.
Rtotal = R1 + R2 +…+ Rn
Capacitance follows the same law as resistance but reciprocated. By this I mean that the reciprocal of the total capacitance is equal to each component’s capacitance reciprocal.
1/Ctotal= 1/C1 + 1/C2 +…+ 1/Cn
The voltage at any point in the circuit can be found by applying Ohm’s law (V=IR) and using the given current, or any components current because they are all the same, and the resistance of the component you are measuring.
Parallel Circuits
These circuits differ from series circuits in that instead of only one path for the current to go, there are as many paths as there are components connected in parallel. This does however mean that the voltage, or potential difference, is the same across all components connected in parallel.
V=V1=V2=Vn
Resistance can be measured similar to the method in which we find the capacitance of a series circuit. It is the reciprocated sum of all resistance components of the circuit.
1/Rtotal = 1/R1 + 1/R2 +…+1/Rn
Just like resistance, finding the capacitance of a parallel circuit is just like finding the total resistance in a series circuit.
Ctotal = C1 + C2 +…+ Cn
To find the total current through a parallel circuit you just apply Ohm’s law, rearranged from the aforementioned form, to each component and add them together.
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