Total Resistance of Parallel Circuit Calculation

In summary, the total resistance of the given arrangement is incorrect as 4.0 Ohms and should be calculated using the series and parallel formulas for R1 and R2, and R1R2 and R3 respectively. The given graphic also shows R3 as 13 ohms instead of 18 ohms. Additionally, the answer should be rounded to one decimal place, and not 4.05.
  • #1
Vaish

Homework Statement


R1= 9 Ohms R2= 17 Ohms R3= 18 Ohms
what is the total resistance of this arrangement? Express answer in ohms, correct to one decimal place.

Homework Equations


I used the Parallel circuit formula 1/r1 + r2 + r3

The Attempt at a Solution


I got 4.0 Ohms, apparently, it is incorrect. Please help. Thank you!
 

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  • #2
R1 and R2 are in series, so use the series formula there.
Then the R1R2 resistors are in parallel with R3, so use the parallel formula with the series result and R3.

Also, in the graphic, R3 is 13 ohms, not the 18 you stated.
The "4.05" in the graphic is apparently your answer:
1) Although the problem asks for 1 decimal place, your answer is shown to two places.
2) Your answer is wrong. It is not 4.05 - it is substantially larger than that.
 
  • #3
Thank you very much. This definitely helped and I also noted the 1 decimal place.
 
  • #4
Vaish said:
1/r1 + r2 + r3
No such formula. What did you mean?
 

1. What is total resistance and why is it important?

Total resistance is the combined resistance of all components in an electrical circuit. It is important because it determines the amount of current that can flow through the circuit and affects the performance of the circuit.

2. How do you calculate total resistance in a series circuit?

In a series circuit, total resistance is calculated by adding together the individual resistance values of each component. RT = R1 + R2 + R3 + ...

3. How do you calculate total resistance in a parallel circuit?

In a parallel circuit, total resistance is calculated using the formula 1/RT = 1/R1 + 1/R2 + 1/R3 + ..., where R1, R2, R3, etc. are the individual resistance values.

4. What is the difference between series and parallel circuits in terms of total resistance?

In a series circuit, total resistance increases as more components are added, while in a parallel circuit, total resistance decreases as more components are added. Additionally, in a series circuit, the same current flows through each component, while in a parallel circuit, the current is divided among the components.

5. How does the total resistance affect the brightness of a light bulb in a circuit?

The total resistance affects the brightness of a light bulb by determining the amount of current that can flow through it. A higher total resistance means less current and a dimmer light bulb, while a lower total resistance means more current and a brighter light bulb.

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