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
solve using voltage division rule

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:
voltage divider can be applied directly here
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:voltage divider - Thevenin equivalent required

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

8 thoughts on “Find Voltage Using Voltage Division Rule

  1. 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?

  2. thank u very much i really enjor dis question goes dos.plz if we hv lyk 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, 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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