Series Circuit and Voltage Division


Series Circuit and Voltage Division

  • Circuit elements are in series if they carry the identical current. The equivalent resistance of resistors connected in series is the sum of the individual resistances.

 


  Example 1: Find the total equivalent resistance in the following circuit

Solution

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  Example 2: For the following circuit:

  1. Find the total resistance
  2. Find the current i
  3. Find the voltage accross the 10Ω resistor

Series 1

Solution

  1. Total resistance

  1. The current can be calculated as

  2. The voltage across the 10Ω resistor

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  Example 3: For the following circuit:

  1. Find the total resister value RT
  2. Find the current i
  3. Find the voltage across the individual resistors
  4. Verify Kirchhoff’s voltage law

Series2

Solution

  1. Total resistor value

  2. The current can be calculated a

  3. The voltage over the resistors


    ,

    ,

  4. To verify the Kirshhoff's Voltage

     

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  Example 4: For the following circuit:

  1. Find V1
  2. Find V2
  3. Verify Kirchhoff Voltage Law around a closed loop

Solution

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Voltage Division:

In the following circuit, the current through all the resistor in series is
The equivalent resistor Req is sum of the resistor value.

To find the voltage drop vi across the resistor Ri, we use current and resistor value

The right side of the equation gives us Voltage division equation.


Examples:

Example 5: For the following circuit

  1. Find the total resister value RT
  2. Find the current i
  3. Find the voltage over resistors
  4. Verify Kirchhoff’s voltage law

Solution

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Example 6: Find the current for the following circuit


Solution

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Practice Problems:

(Click image to view solution)

Problem 1: Find for the following circuit.

View Solution

practice-1.gif

Solution:

Apply Kirchhoff’s Voltage Law


      

Problem 2: Calculate the voltages for the following circuit.

View Solution

practice-2.gif

Solution:

the current,

<

Applying Kirchhoff’s Law :


      

Problem 3: Find the applied voltage to the following circuit using the information provided

View Solution

Solution:


      

Problem 4: Find the resistor R value using the information provided

View Solution

Solution:

or



Problem 5: Find Vx

View Solution

Solution:

      

Exercises:

    Answers:

Survey: