The equivalent resistance for the resistors in this circuit?

In summary: X=9-R3*(1+R3)Y=9+R3*(1-R3)Now combine the two equations and solve for R3.R3=9-(X-Y)*(1+R3)Hence, R3=9+R3*(1-R3).
  • #1
Islam Sabry
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Homework Statement


If the circuit of parallel and series resistors , is as follows , what's the equivalent resistance for the group?

Homework Equations


neglecting the battery internal resistance... irrelevant to the question.

The Attempt at a Solution


I tried to do the following
R1=8+12=20 ohms
R2=4+6=10 ohms
R3=9 ohms
then,
R(equivalent)= R1//R2//R3

but I'm not sure!
 

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  • #2
Ω
Islam Sabry said:

Homework Statement


If the circuit of parallel and series resistors , is as follows , what's the equivalent resistance for the group?

Homework Equations


neglecting the battery internal resistance... irrelevant to the question.

The Attempt at a Solution


I tried to do the following
R1=8+12=20 ohms
R2=4+6=10 ohms
R3=9 ohms
then,
R(equivalent)= R1//R2//R3

but I'm not sure!
I am not sure how the double slashes in R1//R2//R3 are interpreted mathematically. Can you imagine what the potential difference across the 9 Ω resistor might be?
 
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  • #3
means that R1 , R2, and R3 are connected in parallel ... and the question contains no voltage value..sorry if it's vague.
 
  • #4
Islam Sabry said:
R1=8+12=20 ohms
True, but not useful since the current is not flowing through these two in turn.
Create unknowns for all the voltages and currents, write down all the equations, and solve.
 
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  • #5
For this circuit there is an easy way to solve it. Take a look at the resistor values and think about potential dividers and symmetry.
 
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  • #6
Islam Sabry said:

Homework Statement


If the circuit of parallel and series resistors , is as follows , what's the equivalent resistance for the group?

Homework Equations


neglecting the battery internal resistance... irrelevant to the question.

The Attempt at a Solution


I tried to do the following
R1=8+12=20 ohms
R2=4+6=10 ohms
R3=9 ohms
then,
R(equivalent)= R1//R2//R3

but I'm not sure!
Denote the nodes where the 9 Ω resistor is connected as X and Y.

Now imagine the circuit with the 9 Ω resistor temporarily removed. With the 9 Ω resistor gone, write expressions for the voltage at X and the voltage at Y.
 
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What is the concept of equivalent resistance?

The concept of equivalent resistance is the resistance value that represents the total resistance of a circuit with multiple resistors. It is a simplified value that can be used to analyze the behavior of the circuit.

How is equivalent resistance calculated?

The equivalent resistance is calculated by adding the individual resistances in series or using a parallel resistance formula for resistors in parallel. For resistors in series, the equivalent resistance is the sum of all the resistances. For resistors in parallel, the equivalent resistance is calculated using the formula 1/R = 1/R1 + 1/R2 + ... + 1/Rn.

What is the significance of equivalent resistance?

The equivalent resistance allows us to analyze the behavior of a circuit with multiple resistors as a single resistance value. This simplifies the circuit analysis and helps in understanding the overall circuit behavior.

What are the factors that affect equivalent resistance?

The main factors that affect equivalent resistance are the number of resistors in the circuit, their individual resistance values, and their connection (series or parallel). The equivalent resistance will be lower for resistors in parallel and higher for resistors in series.

How does equivalent resistance affect the current and voltage in a circuit?

The equivalent resistance affects the current and voltage in a circuit by determining the overall resistance of the circuit. A lower equivalent resistance will result in higher current and lower voltage, while a higher equivalent resistance will result in lower current and higher voltage. This is based on Ohm's law, which states that current is directly proportional to voltage and inversely proportional to resistance.

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