Series and Parallel Circuits

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

V₁ = (R₁/(R₁ + R₂ + R₃)*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 = V₁ + V₂ + V₃. Resistances in series connection add up directly to give total resistance R _tot = R₁ + R₂ + R₃.

Example

Find the following for the series circuit given below.

1. Total Resistance
2. V₁ and V₂ using a voltage divider
3. Find V₃ using KVL
4. Find the current flowing between R₁ and R₂

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

1. Voltage drop on Parallel connected components remains the same.
2. Current divides among components are connected in Parallel.
3. Resistances in Parallel connection add up reciprocally to give total resistance. 1/R_tot = 1/R₁ + 1/R₂ + 1/R₃
4. The current divider can be used for finding current flowing in different resistors connected Parallel. Current divider formula => I₁ = (R_tot / R₁) * I
5. KCL (Kirchhoff’s Current Law): the total current I_tot that leaves the battery should be equal to the sum of the current in individual branches of a parallel circuit. I_tot I₁ + I₂ + I₃

Example

Find the following for the parallel circuit given below.

1. Total resistance.
2. Value of V₁ and V₂
3. Current in ammeter A₁ and A₂ using V = I * R
4. Find A₃ using the current divider.
5. Find A₄ using KCL.

Resistance Banks in Series

R₃ is connected in series with the parallel combination of R₁||R₂ therefore Current I total must divide between I₁ and I₂ , as R₁ and R₂ are in parallel connection therefore the voltage V₁ and V₂ are of the same value, 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

Wheatstone Bridge