By: Arif Khan.

### Series Circuit

When components are connected in a straight line such that the current flowing in the circuit doesn’t have any other alternative path to flow, the circuit is called a *series circuit.*

#### Node

A node refers to any point in a circuit where two or more devices are connected together.

#### Series Circuit Rules

The current in the series circuit at all points remains the same. Voltage in a series circuit divides by components in the circuit. A voltage divider can be used for finding voltage drops on different resistors connected in series.

#### Voltage Divider Formula

*V _{1} = (R_{1}/(R_{1} + R_{2} + R_{3})*V*

#### KVL (Kirchhoff’s Voltage Law)

The sum of voltage drop on all resistors in a series circuit is equal to applied voltage *V _{EMF} = V_{1} + V_{2} + V_{3}*. Resistances in series connection add up directly to give total resistance

*R*.

_{tot}= R_{1}+ R_{2}+ R_{3}#### Example

Find the following for the series circuit given below.

- Total Resistance
*V*and_{1}*V*using a voltage divider_{2}- Find
*V*using KVL_{3} - Find the current flowing between
*R*and_{1}*R*_{2}

#### Resistance String in Series

Adding resistance of resistors connected in series makes up the string. For example for the circuit given in example above string is 100Ω + 300Ω + 50Ω = *450Ω*

#### Parallel Circuit Rules

- Voltage drop on Parallel connected components remains the same.
- Current divides among components are connected in Parallel.
- Resistances in Parallel connection add up reciprocally to give total resistance.
*1/R*_{tot}= 1/R_{1}+ 1/R_{2}+ 1/R_{3} - The current divider can be used for finding current flowing in different resistors connected Parallel. Current divider formula =>
*I*_{1}= (R_{tot}/ R_{1}) * I - KCL (Kirchhoff’s Current Law): the total current
*I*that leaves the battery should be equal to the sum of the current in individual branches of a parallel circuit._{tot}*I*_{tot}I_{1}+ I_{2}+ I_{3}

#### Example

Find the following for the parallel circuit given below.

- Total resistance.
- Value of
*V*and_{1}*V*_{2} - Current in ammeter
*A*using_{1}and A_{2}*V = I * R* - Find
*A*using the current divider._{3} - Find
*A*using KCL._{4}

#### Resistance Banks in Series

R_{3 }is connected in series with the parallel combination of R_{1}||R_{2} therefore Current I total must divide between *I _{1}* and

*I*, as

_{2}*R*and

_{1}*R*are in parallel connection therefore the voltage

_{2}*V*and

_{1}*V*are of the same value,

_{2}**this is why resistor banks are used to have same voltage on different resistances connected in parallel combination**.

*Resistance Banks and Strings In Series-Parallel*

*Resistance Banks and Strings In Series-Parallel*

#### Wheatstone Bridge