Total equivalent resistance of a combined circuit

AI Thread Summary
The discussion centers on calculating the total equivalent resistance of a combined circuit involving resistors R1, R2, R3, and R4. It was established that R1 is in parallel with the series combination of R2, R3, and R4, which totals 30 ohms. However, there was confusion regarding the correct application of the parallel resistance formula, leading to multiple calculations of equivalent resistance. The correct equivalent resistance was ultimately determined to be 15 ohms when applying the parallel formula accurately. The conversation highlights the importance of correctly identifying resistor configurations in circuit analysis.
dnk3294
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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)
Relevant 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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dnk3294 said:
, 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.
 
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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dnk3294 said:
R2(20)
The problem statement says R2=5Ω
dnk3294 said:
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.
 
dnk3294 said:
R2(20)+R3(10)+R4(15)= 45 Ohms.

Does R2 = 5 ohms or 20 ohms?
 
R2 is equal to 5 ohms.
 
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?
 
dnk3294 said:
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
 

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