series Resistance

 series  Resistance

        Two elements are said to be in series whenever the same current physically flows through both of the elements.  The critical point is that the same current flows through both resistors when two are in series.  The particular configuration does not matter.  The only thing that matters is that exactly the same current flows through both resistors.  Current flows into one element, through the element, out of the element into the other element, through the second element and out of the second element.  No part of the current that flows through one resistor "escapes" and none is  added. 

shows several different ways that two resistors in series

Equation of resistors in series:

The total equivalent resistance of resistors in series is the sum of the resistance values:

R _total= R₁+R₂+ R₃+…………………..

 

• The current through the two resistors is the same.

• The voltage across the series combination is given by:

        Vs= Va + Vb

    The voltages across the two resistors are given by Ohm's Law      :

        Va = Is Ra

        Vb = Is Rb

        We can combine all of these relations, and when we do that we find the following.

    Vs= Va + Vb

    Vs= Is Ra  + Is Rb

    Vs= Is (Ra  + Rb)

    Vs= Is Rseries

Example 

Using Ohms Law, calculate the equivalent series resistance, the series current, voltage drop and power for each resistor in the following resistors in series circuit.

 

 

All the data can be found by using Ohms law, and to make life a little easier we can present this data in tabular form.

Resistance	Current	Voltage	Power
R1 = 10Ω	I1 = 200mA	V1 = 2V	P1 = 0.4W
R2 = 20Ω	I2 = 200mA	V2 = 4V	P2 = 0.8W
R3 = 30Ω	I3 = 200mA	V3 = 6V	P3 = 1.2W
RT = 60Ω	IT = 200mA	VS = 12V	PT = 2.4W

 

 

Then for the circuit above, 

R_t=R₁+R₂+R₃

R_t=10+20+30=60Ω

, I_T = 200mA, V_S = 12V and P_T = 2.4W