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How to calculate resistors in series and parallel

In this post, you will learn how to calculate resistors in series and parallel. First of all, we shall  be analyzing resistors’ networks that are in series connections and perform some calculations. After this, the analysis and calculations of resistors in parallel.

RESISTORS IN SERIES
Things you should know when resistors are connected in series.

In this configuration, the resistors are connected end to end so that the same current (I) passes through all of the resistors.

When a network or circuit is setup by different resistors connected in series, the total resistance of the network or circuit is equal to the sum of the resistance of each resistor.

There will  be a voltage drop across each of the resistor in the network.

The sum of those voltages dropped across each resistor in the series network gives the total potential difference (Pd) across the network.

Resistors in Series

Resistors in series mathematical 1

Since the same current passes through all the resistors when connected in series, therefore the formula for individual voltage drops across each of the resistors is written thus;

According to Ohm’s Law; (V=IR) therefore;

Resistors in series mathematical 2

Example 1

A 3Ω resistor and a 2Ω resistor are in series connection and a potential difference (Pd) of 100V is exists across them. Fine:

  1. The equivalent resistance of the circuit
  2. The current that flows in it
  3. The potential difference across each resistor.

Solutions

The successful ways for the solution of this problem is below. So,

Resistors in series calculation circuit

(a) The equivalent resistance of the circuit is thus;

Resistors in series mathematical 3

This is more than of either of the resistors

(b) The current in the circuit is, from Ohm’s Law

Resistors in series mathematical 4

(c) The potential difference across R1 is;

Resistors in series mathematical 5

Note that the sum of V1 and V2 =100V, which is certainly the total potential difference in the circuit.

Also, I have placed an exercise for you!

Exercise

Consider the network of three resistors connected in series to each other given that; R1=4Ω, R2=2Ω, and R3=1Ω. If the total current (I) in the network is 2.5A, calculate;

  1. The total equivalent resistance
  2. Voltage drop across each of the resistors
  3. The total potential difference (Pd) across the whole network.
RESISTORS IN PARALLEL

In this configuration, the resistors are connected side by side with their ends joined together. In this way, the same potential difference V exists across each resistor. As a result of this, the resistors share the main current in the circuit. Smaller current will flow through the resistor with larger value of resistance. Also, large current will flow through the resistor with lower value of resistance.

Notes to take when resistors are connected in Parallel
  1. Reciprocal of the equivalent resistance of a set of resistors connected in parallel is equal to the sum of the reciprocals of the resistance of each resistors.
  2. In this connection, the same potential difference (V) exists across each of the resistor.
  3. Different current passes through each of the resistors.
  4. The total current is the sum of the currents passing through each of the resistors.

The figure below shows Resistors in Parallel

Resistors in Parallel

Resistors in parallel formulae

Resistors in Parallel Mathematical

The LCM of the right-hand side of this formula is R1R2R3, which therefore enables us to write:

Taken the reciprocal of both sides of this equation therefore yields the convenient result. Thus;

Total current is the sum of currents through each resistor. Therefore;

Since the potential difference (V) is the same across all the resistors, and by applying Ohm’s Law to each of them in turn, we finally find that;

The smaller the resistance, the greater the proportion of the total current that will flows through it.

Resistors in Parallel Calculations
Example:

A 3Ω and a 2Ω resistor are connected in parallel respectively and a potential difference of 100V is applied across them. Find the equivalent resistance of the circuit. Find also the current that flows in each resistor and in the circuit as a whole.

Solution

Resistors in series calculation

(a) The equivalent resistance of the resistors is;

(b) The current that flows in R1 is;

And the current that flows through R2 is

The total current in the circuit is therefore;

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