Find Voltage Using Voltage Division Rule

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Electrical Circuits, Electrical Circuits Problems, Resistive Circuits

Determine voltage across $R_2$ and $R_4$ using voltage division rule.
Assume that
$V_1=20 V$ , $R_1=10 \Omega$ , $R_2=5 \Omega$ , $R_3=30 \Omega$ and $R_4=10 \Omega$

Solution:
Please note that the voltage division rule cannot be directly applied. This is to say that:

$V_{R_3} \neq \frac{R_1}{R_1+R_3} V_1$
The reason is that some current of $R_1$ is passing through $R_2$ and $R_4$ branch. If the branch was broken at some point, for example as:

we could apply the voltage division rule and say
$V_{R_3} = \frac{R_1}{R_1+R_3} V_1$
But for the original circuit, the equation above is not correct. To solve the circuit using the voltage divider, we have to find the Thevenin equivalent of the colored circuit:

$R_2$ and $R_4$ are in series and their equivalent equals $R_{24}=R_2+R_4=5 \Omega + 10 \Omega = 15 \Omega$

$R_3$ and $R_{24}$ are parallel and their equivalent equals $R_{324}=R_3||R_{24}=30 \Omega || 15 \Omega = \frac{30 \times 15}{30 + 15}=10 \Omega$
So, the circuit is simplified to this level now:

And the voltage division rule can be applied directly:
$V_{R_{324}}=\frac{R_{324}}{R_{324}+R_1} V_1=\frac{10}{10+10} 20=10 V$
Please note that $V_{R_{324}}$ is the voltage across $R_3$ and the series combination of $R_2$ and $R_4$ as shown below:

Now, we can use the voltage division rule to find $V_{R_2}$ and $V_{R_4}$ . We can ignore the rest of the circuit and assume that this portion is as:

and write:
$V_{R_2}=\frac{R_2}{R_2+R_4} V_{R_{324}}=\frac{5}{5+10} 10=\frac{10}{3} V$

$V_{R_4}=\frac{R_4}{R_2+R_4} V_{R_{324}}=\frac{10}{5+10} 10=\frac{20}{3} V$

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Comments

10 responses to “Find Voltage Using Voltage Division Rule”

August 13, 2014

abdur rauf

thanks for this site

Reply
August 20, 2014

abebaw

TANKS

Reply
November 7, 2014

Athulya Nair

Hi,

Thanks for this site. As this helps me solve Network Theorems circuits easily.

Reply
December 17, 2014

ibrahim

Where current
Erro why
Buz i=1A
Req= 20

Reply
January 12, 2015

Natalie

Wait, so does this mean to find $V_3$ it would be:

$V_{R_3} = \frac{ R_3 \times V_{324} }{ R_1 + R_2 }$

If this were the case the answer would be 15/2?

Reply
1. April 18, 2015
  
  Yaz
  
  No, this is not correct.
  
  Reply
January 28, 2015

olanrewaju ibrahim

thank u very much i really enjor dis site.my question goes dos.plz if we hv lyk 10resistor.in.a circuit diagram dt dy are in series nd parallel.wt 10 volt.thats we hv five loop.the question nw say.using circuit diagram above,calculate.the value of current in 10k resistor.using thevenin theorem,norton thorem.kvl nd kcl.principle.replace d branch a,b,c,d.show dat d transfer resistance of d circuit remain d same.are we going to use circuit reductions fo it.thanks.nd i will be happy if u can help me to solved it wt any circuit dt have up to ten resistor.thank uGod bless

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February 2, 2015

togara ishmael

so nce

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January 13, 2019

samer

vielen dank
thank you
شكرا جزيلا

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June 25, 2019

Charles

thanks for the site.

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