# Series and parallel circuits

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## Contents

[show]#### CircuitsEdit

A circuit is a closed path for the flow of charge. It usually contains a source of potential difference and a resistor; it may have other devices such a voltmeter or an amp meter. There are two types of circuits; the series circuit is one that only has one path for the current to flow through. The other type of circuit is the parallel circuit, which has more than one path for the current to flow through.

A current is the flow of charge, the speed of the particles is not measured instead the quantity of the particles that pass through at a single point in time. The current is measured in ampere (I). An ampere is equal to 1 coulomb per second(C/s). The particles that move are the electrons, which contain negative charges. The positive which is what we measure is known as conventional current. The convention current is the same as the electron flow except for its direction.

The battery/source of potential difference is where the current usually begins. Without a source there will be no current. It is represented by two lines. The is longer than the other. The shorter line is the negative side of the source, while the longer one positive. This gives the circuit a certain voltage (v)

Another part of the current is the wire. This is the media through which the current flows through. The wire usually has an extremely low resistance and therefore it is negligible.
A resistor is where most of the resistance is concentrated. It can be calculated as the ratio of the voltage of the circuit to the current.

The resistance can also vary depending on the temperature, length and area of the resistor.

*p*(L/A)

L is equal to the length of the resistor; A represents the area of the given resistor. The p stands for the resistance of the material used for the resistor. In order to get the new resistance you must multiply the resistance of the material by it length and divide that by the area.

#### Series CircuitEdit

As stated previously a series circuits have only one path for the current to flow through. Therefore if one of the regions is removed then the entire circuit stops working

Here is a simple series circuit the. The pink squiggly line represents a resistor
The gray box represents the battery. Also known as the source of potential difference. The gray arrows labeled I show flow of the current

This circuit is the simplest type of series circuit. In most cases there will be more than one resistor or question will ask you to find the current or the voltage. A series circuit has rules to follow in order to figure this out. Most circuits follow Ohm’s law.

This is another version of the resistance equation.
The circuits that follow this law are called Ohmic circuits, while the one that don’t follow this law are called nonohmic circuits

As stated there may be more then one resistor in the circuit. In order to use the equation above we must find the total resistance of the system also known as the R_{eq}In order to find the R_{eq} for a series circuit you simply add all the resistors together.

_{eq}= R

_{1}+ R

_{2}+ R

_{3}… + R

_{n}

The same equation also applies for the voltage of a series circuit. to get the total voltage of a series circuit.

_{ttl}= V

_{1}+ V

_{2}+V

_{3}…+ V

_{n}

On the other hand the current in series circuit remains constant no matter where it is measured

_{ttl}= I

_{1}= I

_{2}= I

_{3}…= I

_{n}

#### Parallel CircuitsEdit

Parallel Circuits are circuits that have more than one pat, so the current has a “choice” as to which path to use. Ohm’s law remains the same for parallel circuits. But all the other equations, which determine the individual components (voltage, current, resistance) of ohm’s law differ

The Voltage in a series circuit remains the same, throughout the system

_{ttl}= V

_{1}= V

_{2}=V

_{3}…V

_{n}

The current on the other hand does not stay constant. To find the total resistance all the currents must be added together.

_{ttl}= I

_{1}+ I

_{2}+ I

_{3}+ … I

_{n}

The resistance is the one that is the most different. In order to find the total resistance of a parallel circuit, you must take the reciprocal of each individual resistance, then add these fractions up, and take the reciprocal of the final answer. This is the total resistance in the system.

_{eq}= R

_{1}

^{-1}+R

_{2}

^{-1}+…R

_{n}

^{-1}

#### Parallel and Series CircuitsEdit

When dealing with circuit which contain both parallel and series parts, it is important to solve the equations in the right order in order to receive the correct answer. First you must solve for all the parallel parts of the circuits using the equations for the parallel circuits. Next simply solve the circuit using the series equations. It is important to do it in this order because when you solve the parallel circuit, you receive one resistance number for each parallel part. And then are left with a series circuit. This is easy to solve, because the equation just involve straight addition.

#### PowerEdit

Power of a circuit is the rate at which energy is supplied to the circuit. This can be determined by the equation

P represent the power of the circuit, V is the voltage of the system and I is the current
This equation can be written in many different ways, by the use of substitution.
According to Ohm’s law V = IR. If we substitute this value in for V, we get

^{2}R

Or if we use the equation I = V/R. we get the equation

^{2}/R