# Total equivalent resistance of a combined circuit

#### dnk3294

Homework Statement
Three light bulbs are connected in a circuit as shown in the diagram. Vs= 15V, R1= 30 ohm, R2= 5 ohm, R3= 10 ohm, R4= 15 ohm. Determine the total equivalent resistance (Req)
Homework Equations
1/Req= 1/R1+1/R2+1/R3 for parallel resistors.
R= R1+R2+R3 for resistors in series.
I attempted to solve the problem by following the positive terminal of the battery and I realized that Resistor R1 has a different path than R2+R3+R4. I came to the conclusion that R1 is in parallel with R2+R3+R4. The series connection with R2,R3,R4 would be 30 ohm total by adding the three resistors. To find the equivalent resistance, I added 30 ohm to the resistance of a parallel resistor which was 1/Req= 1/30 and Req=30 ohm. The total equivalent resistance was calculated to be 60 ohm.

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#### haruspex

Homework Helper
Gold Member
2018 Award
, I added 30 ohm to the resistance of a parallel resistor which was 1/Req= 1/30 and Req=30 ohm. The total equivalent resistance was calculated to be 60 ohm.
You do not seem to have applied that formula correctly. Please post the details of that calculation.

#### dnk3294

Sorry about the error, I thought that R2,R3,R4 were in series so the resistors in series would equal:
R2(5)+R3(10)+R4(15)= 30 Ohms.
R1 is in parallel so it would be :
1/Req= 1/30 = 30 Ohms.
The total equivalent resistance would be 30ohms +30 ohms=60 ohms.

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#### haruspex

Homework Helper
Gold Member
2018 Award
The problem statement says R2=5Ω
R1 is in parallel so it would be :
1/Req= 1/30 = 30 Ohms.
No, you are not using the parallel resistance formula correctly.
Having merged R2, R3 and R4 into the single equivalent resistance R=R2+R3+R4 you have simplified it to R1 in parallel with R. How do you combine two resistors in parallel? The formula you quoted in post #1 is for combining 3.

#### Master1022

R2(20)+R3(10)+R4(15)= 45 Ohms.
Does R2 = 5 ohms or 20 ohms?

#### dnk3294

R2 is equal to 5 ohms.

#### dnk3294

Would the equivalent resistance be :
1/Req= 1/30+1/30 = 2/30 and the answer would be 15 ohms for the equivalent resistance due to R and R1 being in parallel?

#### Master1022

Would the equivalent resistance be :
1/Req= 1/30+1/30 = 2/30 and the answer would be 15 ohms for the equivalent resistance due to R and R1 being in parallel?
yes

"Total equivalent resistance of a combined circuit"

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