Electronic – Equivalent resistance of circuit

circuit analysismultisimresistanceresistorssimulation

I have a simple resistor circuit that i would like to know the equivalent resistance of(as seen from the multimeter terminals):
enter image description here

The image is from Multisim and the resistance is here measured using simulation. I am not sure about the calculation by hand, but my bet is(from right side of the circuit):

(R10+R9+R8)+(R5||R7)+((R6+R2+R1)||(R4+R3))

Which equals:

enter image description here

This is close to the simulated result, but I am not sure if my equivalent calculation is correct.Do I need to apply a Star/Delta ? Can anyone state a correct method of solving this or come up with the correct answer with working ?

Best Answer

That circuit can be simplified only to a point by using only series/parallel transformations. By using those you end up with this circuit:

enter image description here

where \$R12 = R1 + R2 \$, \$R34 = R3 + R4\$ and \$Rs = R8 + R9 + R10\$.

As you can see no further reduction can be done with series or parallel transformations.

At this point you have two possibilities:

  1. Apply a voltage source to the terminals, calculate (using mesh analysis, for example) the current drawn by the circuit and calculate the equivalent resistance as V/I.

  2. Simplify the circuit further applying the so called star/delta transformations.

With the second approach you need in particular these formulas to transform, for example, the delta connection of R5, R6 and R7 into a star connection. Once you do this, the circuit can be further simplified using usual series/parallel transformations.

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