# Find Voltage Using Voltage Division Rule

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

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

Hi! Yaz is here. I am passionate about learning and teaching. I try to explain every detail simultaneously with examples to ensure that students will remember them later too.

## Join the Conversation

1. abdur rauf says:

thanks for this site

2. abebaw says:

TANKS

3. Athulya Nair says:

Hi,

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

4. ibrahim says:

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

5. Natalie says:

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?

1. No, this is not correct.

6. olanrewaju ibrahim says:

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

7. togara ishmael says:

so nce

8. samer says:

vielen dank
thank you
شكرا جزيلا

9. Charles says:

thanks for the site.