Linear Circuit Analysis

What is voltage divider

A voltage divider is method which is  used to calculate the voltage across desired elements

Yes of course we do have ohm’s law but using voltage divider is more easy . First wee don’t need to find current individually and secondly we don’t need to calculate the voltages individually

For example

In following circuit , if I need to find total combined voltage in R3 and R4. I will do the following steps.

• 1. FinD Rt
• 2. Find total Current
• 3. Find individual voltage
• 4. Add R3 and R4 voltages

How ever in VDR we can solve this using a simple formula

Voltage Divider EQUATION

Lets say we need to find a voltage across particular resistor in a circuit,, we can easily apply ohms law

VR=I total x R….                            Equation 1

Where as I total = Vtotal/Rtotal…  Equation 2

Putting I total value from Equation 2 to Equation

VR=*R ……………………. Voltage Divider Equation

Example 2.

Find the Vab and Vac using VDR

Solution

Step 1 . Find Total Resistance = 100K+200K+150K+50K=500K

Step 2. Find Rab and Rac = (Rab=200K) and (Rac=350K)

Step 3 Calculate Vab

Vab =

=14.4 V

Step 4 Calculate V Ac

=25.2V

Example 2

An Electronic device is to be connected across R2. The Electronic device needs 5 V and I should always be less than 10 mA. Find the Value of R1 .

Solution

We Know I=

In our case the current value should never go above 10 mA

<10mA

Where Value of V= 24 V

<10mA

Calculating R using above equation 

R>2.4 KΩ

• · Here we know that Rt (R1+R2) should be greater than 2.4KΩ. Now its up to us what value we choose for R1 and R2 .
• · The values should be chosen in such a way that R1 and R2 sim should be regather than 2.4kΩ
• · So I am going to choose R2 as 2.4 KΩ as it will sataisfy the equation that R1+R2>2.4 KΩ.
• You may choose any oyher values which satisfy this equation

Using VDR Formula

We know we know 5 Volts from Vt(24V) across Resistor R2 (2.4kΩ). Putting Values in formula

=5V

=5V

Rtotal= 11.52 KΩ

Rt=R1+R2

11.52kΩ=R1+2.5KΩ

R1=9.12 kΩ

Potentiometers and Rheostats

A Potentiometer is adjustable voltage divider. It is a three terminal device with a wiper or a slider in between. The wiper and slider is moved to increase and decrease the value of resistance

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Its Symbol is

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.Types of Potentiometer

Potentiometers comes in different shapes sizes and colors, Few are large enough that they  can be held in hand , while other are very small (smaller than your nail), Few value can be adjusted by  A know , some have to be adjusted with screw driver. Similarly some are linearly straight , while other are rotary. Both have a wiper arm , which can be moved to adjust value 

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So lets try ……. Few examples

Choose the answer

Example

Find the voltage range v1 and v2 .

Now the important thing to notice here is that V1 is across a potentiometer , so the voltage across it will vary as we will move pot up and down . So we need to find Vmin (R min) and Vmax (R max) to find the range .

Solving for R min

• Rmin=0
• Total resistance of a circuit is now = R1+R2+R3
• =5k+0+10k

         =15k

Finding V1 (using VDR, When R=0

= (0/15k)*24= 0 Volts

Solving for R max

• Rmin=10K
• Total resistance of a circuit is now = R1+R2+R3
• =5k+10k+10k

          =25k

Finding V1 (using VDR, when R=Rmax)

= (10/25)*24= 9.6 Volts