Find the equivalent resistance of a circuit below

In summary, the equivalent resistance of the circuit is 20 ohm, calculated by combining the resistors in series and then parallel. The correct equations to use are 1/R56 + 1/R4 = 1/R456 and 1/R3456 + 1/R2 = 1/R23456. The resistors are of equal value and can be substituted in the equations to find the equivalent resistance.
  • #1
shashaeee
30
0
Find the equivalent resistance of the circuit shown below. Each of the six resistors has a resistance of 12 ohm.
physics.jpg


I just want to make sure I calculated everything right. I don't have the solution available.

Labelling the resistors from my left to the right: R1, R2, R3, R4, R5(bottom), R6

What I did:

R5 + R6 = R56

1/R56 + 1/R4 = R456

R456 + R3 = R3456

1/R3456 + 1/R2 = R23456

R23456 + R1 = Req = 20Ω

Thanks!
 
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  • #2
Your logic all looks correct to me. I don't have a calculator available, but your work looks fine and the answer seems reasonable.

Edit: The post below me is correct, I missed those errors.
 
Last edited:
  • #3
shashaeee said:
1/R56 + 1/R4 = R456

No, 1/R56 + 1/R4 = 1/R456


1/R3456 + 1/R2 = R23456

No, 1/R3456 + 1/R2 = 1/R23456
 
  • #4
The resistors are of equal value.
In calculation this value is substituted in the equations.
R5+R6=2R
Next the parallel resistor
2R.R/(2R+R)=2R/3
And the next configuration till R1
 
  • #5
Thanks guys!
 

1. What is equivalent resistance?

Equivalent resistance is the total resistance of a circuit when multiple resistors are connected in series or parallel.

2. How do you calculate equivalent resistance?

The equivalent resistance of resistors in series is the sum of their individual resistances. The equivalent resistance of resistors in parallel is calculated using the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistances.

3. Can you simplify a complex circuit to find equivalent resistance?

Yes, a complex circuit can be simplified by identifying series and parallel combinations of resistors, and then calculating the equivalent resistance of each combination. The equivalent resistances can then be combined until the final equivalent resistance is found.

4. Is equivalent resistance the same as total resistance?

Yes, equivalent resistance and total resistance refer to the same concept. It is the resistance that a single resistor would need to have in order to produce the same amount of current as the entire circuit.

5. What factors can affect the equivalent resistance of a circuit?

The factors that can affect the equivalent resistance of a circuit include the number and arrangement of resistors, the material and length of the resistors, and the temperature of the circuit. Changes in any of these factors can alter the overall resistance of the circuit.

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