Resistors in Series

Series Circuit of Resistors: When two or more conductors having resistance R1 , R2 …. are joined together with one end of resistor connecting one end of another resistor as shown on figure below then the circuit thus formed is said to be a series circuits of resistors.

The characteristics of a series circuit of resistors are:

  • Same current flows through each of the resistors.
  • Each resistor have their own corresponding voltage drop.
  • Voltage drops are additive or the total voltage applied is equal to the sum of voltage dropped in each resistors.
  • Resistances are also additive or the total resistance of the circuit is the sum of resistance of each resistor.
  • Powers are also additive or the total power consumed by the circuit is the sum of power  consumed by each of the resistors

Resistors in Series.

It can easily be proved that the total resistance of a series circuit is the sum of resistance of individual resistors in he circuit:

Voltage,Current and Resistance in series circuit
Voltage,Current and Resistance in series circuit

 

In the image above:

V = Total Applied voltage.

R1 , R2 , R3 ..=  Resistance of resistors.

V1 , V2 , V3 … = the voltage dropped in corresponding resistors.

and R = total equivalent resistance of the Circuit.

V = V_1 + V_2 + V_3 + V_4 = IR_1 + IR_2 + IR_3 + IR_4

and also V = IR

or, IR = IR_1 + IR_2 + IR_3 + IR_4

Thus , R = R_1 + R_2 + R_3 + R_4

Opens in a Series Circuit:

In a normal series circuit as shown in the first figure (a) below , there is normal flow of current across the resistors. But when the circuit is opened due to various reasons like blown fuse , blown components , wire cuts etc as shown in the second figure (b) below:

open in a series circuit
open in a series circuit

Then the following effects will take place:

  1. There will be no current flow through the circuit so the circuit will stop working because of the infinite resistance presented by the open.
  2. and The voltage drop across the open will be almost equal to the voltage supplied because of very low resistance offered by other resistors as compared to the infinite resistance of the open.

Shorts in a Series Circuit:

short in a series circuit
short in a series circuit

A short can occur in a series circuit because of excess naked wires or because of loosely placed electrical components as shown on the image above. A short might cause excess flow of current in the circuit. Because a short decreases the total resistance of the circuit it causes excess flow of current and in many cases the excess flow of current can also cause heat and can also cause fire.