# Total equivalent resistance of a combined circuit

• dnk3294
In summary, the problem involved finding the equivalent resistance of a circuit with resistors R1, R2, R3, and R4. By simplifying the circuit, it was determined that R1 was in parallel with R2+R3+R4, with a total equivalent resistance of 15 ohms.
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)
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.

Last edited:
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.

Last edited:
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

## What is the total equivalent resistance of a combined circuit?

The total equivalent resistance of a combined circuit is the overall resistance that an electric current experiences when flowing through a combination of resistors in a circuit. It is the equivalent of a single resistor that would produce the same overall effect on current.

## How is the total equivalent resistance of a combined circuit calculated?

The total equivalent resistance of a combined circuit can be calculated using the formula Req = R1 + R2 + R3 + ... where R1, R2, R3, etc. are the individual resistances in the circuit. This formula applies to both series and parallel circuits.

## What is the difference between series and parallel circuits?

In a series circuit, the resistors are connected end-to-end, creating a single path for the current to flow through. In a parallel circuit, the resistors are connected side-by-side, creating multiple paths for the current to flow through. This affects how the total equivalent resistance is calculated.

## What happens to the total equivalent resistance in a series circuit?

In a series circuit, the total equivalent resistance is equal to the sum of the individual resistances. This means that as more resistors are added in series, the total equivalent resistance increases.

## What happens to the total equivalent resistance in a parallel circuit?

In a parallel circuit, the total equivalent resistance is less than the smallest individual resistance. This means that as more resistors are added in parallel, the total equivalent resistance decreases.

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