Equivalent Resistance of a Ciruit

In summary, the circuit shown has equivalent resistance of 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5 + 1/R6 + 1/R7.
  • #1
Kajayacht
29
0
1. Find the equivalent resistance of the circuit as shown in the diagram below; where R1 = 1 Ω, R2 = 2 Ω, R3 = 2 Ω, R4 = 4 Ω, R5 = 1 Ω, R6 = 1 Ω, and R7 = 2 Ω.
[URL]http://img21.imageshack.us/i/prob06v2.gif/[/URL]

http://img21.imageshack.us/i/prob06v2.gif/

Homework Equations



R(parallel) 1/R(total) = 1/R1 + 1/R2
R(series) R(total) = R1 + R2

The Attempt at a Solution



I know I can do this one, its easy. But the arrangement of the resistors is throwing me off

I think I can take R3 and R4 in series, then take R5 in parallel with R3,4, take that in series with R2.

Then R7 and R6 are in series, and R7,6 is in parallel with R1. R1,7,6 in series with R2,5,3,4

Is this right?
 
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  • #2
not 100% on this but here's my help. id do r3,4 in a series, then Rt of that with r5 in a parallel. then the rt3,4,5 with R2 in a series. r7 and r6 are a series so just add those. then i believe you can just do the 3 final resistances all in one parallel circuit.
 
  • #3
Kajayacht said:
I know I can do this one, its easy. But the arrangement of the resistors is throwing me off

I think I can take R3 and R4 in series, then take R5 in parallel with R3,4, take that in series with R2.

Then R7 and R6 are in series, and R7,6 is in parallel with R1.

This is correct.

Kajayacht said:
R1,7,6 in series with R2,5,3,4

Is this right?

This is not correct.
 
  • #4
After you have added together R7 and R6, you should have 3 resistors in parallel:
1. R1
2. R6 + R7
3. The resistor you got from merging R2, R3, R4 and R5

Use the parallel resistor formula on all three to get R Total

Kajayacht said:
...the arrangement of the resistors is throwing me off

When I used to have this problem, I found that redrawing the circuit makes it easier to see which resistors are in parallel :)
 
  • #5
is what i wrote correct?
 
  • #6
Thanks guys, I got it now. R1,7,6 should be in parallel with R2,5,3,4 not series.
 

Related to Equivalent Resistance of a Ciruit

What is equivalent resistance of a circuit?

The equivalent resistance of a circuit is the total resistance that a single resistor would need to have in order to produce the same current as the entire circuit.

How is equivalent resistance calculated?

Equivalent resistance can be calculated using Ohm's law, which states that resistance (R) is equal to voltage (V) divided by current (I). This can also be calculated using Kirchhoff's laws and the series and parallel resistor formulas.

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 current to flow. In a parallel circuit, the resistors are connected side-by-side, creating multiple paths for current to flow.

How does adding resistors in series affect equivalent resistance?

When resistors are added in series, the equivalent resistance increases as the total resistance of the circuit is the sum of each individual resistor's resistance.

How does adding resistors in parallel affect equivalent resistance?

When resistors are added in parallel, the equivalent resistance decreases as there are multiple paths for current to flow, reducing the overall resistance of the circuit.

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