How do I calculate the equivalent resistance for this circuit?

In summary, the problem involves finding the equivalent resistance of a circuit with multiple resistors. The first step is to combine resistors R4 and R5, and R6 and R7, in series. Then, resistors R4 and R5 are combined in parallel with R8, and R6 and R7 are combined in parallel with R9. The resulting resistors Ra and Rb are then combined in series, and the resulting resistor is in parallel with R2. Finally, the whole group is in series with R1 and R3, giving the equivalent resistance of the circuit as R1 + Rgroup + R3.
  • #1
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I'm in a intro to circuits class for non-EE majors. One of the homework problems asks for the equivalent resistance.

See the attached file for a picture of this system.

I know the first step is to add resistors R4 and R5 (in series) as well as add resistors R6 and R7 (in series). But after that I'm stuck. I think I have to apply a delta (triangle) to Y transformation but I'm not sure how to proceed with it. Any help would be greatly welcomed.

P.S. Please don't tell me the rules for series and parallel circuits. I know what the are I just don't know which resistors to combine in this example.
 

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  • #2
I don't see how a delta y transformation would help you much. I would just start grouping resistors, R4 and R5, then R45 and R8, then the same thing on the bottom, etc.
 
  • #3
Resistors which are end-to-end can be combined as one in series, e.g. R45 = R4 + R5 and R67 = R6 + R7, as StatusX mentioned.

Resistors (or group) which share common nodes or junctions are combined in parallel.

Thus R45 is parallel with R8 giving Ra, and R67 is parallel with R9 giving Rb.

Then Ra and Rb are in series because they are end to end.

Rab is then in parallel with R2,

and the whole group (Rgroup) is in series with R1 and R3.

Req should have the form R1 + Rgroup + R3.
 

FAQ: How do I calculate the equivalent resistance for this circuit?

What is equivalent resistance?

Equivalent resistance is the resistance value of a single resistor that would produce the same total resistance as a combination of multiple resistors in a circuit. It simplifies the circuit and makes it easier to calculate the overall resistance.

How do you calculate equivalent resistance for resistors in series?

To calculate equivalent resistance for resistors in series, simply add up the resistance values of each resistor in the circuit. This is because the current in a series circuit is the same throughout, so the total resistance is equal to the sum of the individual resistances.

How do you calculate equivalent resistance for resistors in parallel?

To calculate equivalent resistance for resistors in parallel, use the formula 1/Req = 1/R1 + 1/R2 + 1/R3... where Req is the equivalent resistance and R1, R2, R3... are the individual resistance values. This is because the voltage in a parallel circuit is the same across each resistor, so the total resistance is inversely proportional to the sum of the reciprocals of the individual resistances.

Why is finding equivalent resistance important in circuit analysis?

Finding equivalent resistance is important in circuit analysis because it simplifies the circuit and allows for easier calculations of voltage, current, and power. It also helps to determine the overall effectiveness of a circuit and whether it will function properly.

Can equivalent resistance ever be lower than the smallest resistor in a circuit?

No, equivalent resistance can never be lower than the smallest resistor in a circuit. This is because adding any additional resistors in parallel will decrease the overall resistance, but it will never be lower than the value of the smallest resistor in the circuit.

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