Resistance with resistors between parallel resistors

In summary, the overall resistance of the circuit is 12.5Ω. To calculate the value of the resistor labelled R, you can use the equation 1/R = 1/R1 + 1/R2 for parallel resistors and the equation R = V/I for calculating resistance from voltage and current. By treating the left-hand side network as a series of 3 resistors (5, 1, and R) in parallel with a 10Ω resistor, we can set up an equation and solve for R.
  • #1
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Homework Statement


The overall resistance of the circuit is 12.5Ω. Calculate the value of the resistor labelled R in the circuit.
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Homework Equations


1/R = 1/R1 + 1/R2
R = V/I

The Attempt at a Solution


I understand that you use the first equation for parallel resistors and the second to calculate resistance from voltage and current. The bit I am having trouble with is the network of 4 resistors on the left hand side. The resistance on the right hand-side is 1/R = 1/2 + 1/6, so R = 1.5. So then 12.5 = 6 + 1.5 + the resistance of the left hand-side network.

I just need guidance on how to calculate it because it puzzles me as there is 2 resistors between the other 2 in parallel.
 
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  • #2
TiernanW said:
there is 2 resistors between the other 2 in parallel.
A matter of drawing; one could also say there are three in series with one in parallel ...
 
  • #3
TiernanW said:
2 resistors between the other 2 in parallel.
Are you sure?
Hint:Current through series resistors is same.
 
  • #4
I find it helpful to follow the current around the circuit. Start at the battery. As the current flows where does it split? It's enough to start at the point in the circuit where you lost the bubble.
 
  • #5
Thanks guys! Just considered the other 3 (5, 1 and R) as a series and the 10 as parallel with those. :)
 
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  • #6
TiernanW said:
The resistance on the right hand-side is 1/R = 1/2 + 1/6, so R = 1.5. So then 12.5 = 6 + 1.5 + the resistance of the left hand-side network.

Yes that's ok.

TiernanW said:
Thanks guys! Just considered the other 3 (5, 1 and R) as a series and the 10 as parallel with those. :)

Yes that's ok for the "left hand side network".

Just turn it all into an equation and solve for R
 

What is resistance in a circuit?

Resistance is a measure of how much a material or component impedes the flow of electric current. It is measured in ohms (Ω) and is represented by the symbol R.

How do resistors affect resistance in a circuit?

Resistors are electronic components that are used to control the amount of current flowing through a circuit. When resistors are placed in parallel, they reduce the total resistance in the circuit, allowing more current to flow.

What is the formula for calculating resistance in a parallel circuit?

The formula for calculating total resistance in a parallel circuit is 1/RT = 1/R1 + 1/R2 + 1/R3 + ... where RT is the total resistance and R1, R2, R3, etc. are the individual resistances of each parallel resistor.

How do you determine the equivalent resistance of parallel resistors?

To find the equivalent resistance of parallel resistors, you can use the formula RT = (R1 * R2 * R3 * ...) / (R1 + R2 + R3 + ...). This will give you the total resistance of the parallel resistors.

What is the purpose of using parallel resistors?

Parallel resistors are used in circuits to reduce the overall resistance and allow more current to flow through the circuit. They can also be used to divide the voltage in a circuit and provide different voltage levels to different components.

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