Find the equivalent resistance (Req) of the simple circuit.

[sugz]

Homework Statement

What is the equivalent resistance between points a and b in the Figure shown.

Homework Equations

Equivalent of two resistors (e.g R1 and R2)= R1*R2/(R1+R2)
Equivalent of two resistors (e.g R3 and R4) = R3+R4

The Attempt at a Solution

Step 1: 6, 12 and 4 ohm resistors are in parallel, which results to 2 ohms.
Step 2: the 2 ohm resistor and the 3 ohm resistor are in series, which results to 4 ohm.
Step 3: Now we have the following circuit.

[/B]
This was slightly confusing. Since there is a short circuit parallel to the 10 ohm resistors, current will flow from point a through the 4 ohm resistor then through the 3 ohm resistor. The current will bypass the 10 ohm resistor and hence it will be ignored in the equivalent resistance calculation. 4 ohm in series with 3 ohm resistor = 7 ohms.

I know the answer is correct (7 ohm) but I would like to confirm my concept regarding the short circuit wire is correct.

 

[robphy]

I think your Step 2 has a slight error in its justification.
Yes, the 10 ohm resistor can be ignored... since it is shorted... that is to say, the voltage drop across that 10 ohm resistor is zero.

[edit:
You can also say that the 10 ohm is in parallel with the 0 ohm...
so R_eq for that parallel combination is (10)(0)/(10+0)=0 ohms.]

 

[sugz]

I think your Step 2 has a slight error in its justification.
Yes, the 10 ohm resistor can be ignored... since it is shorted... that is to say, the voltage drop across that 10 ohm resistor is zero.

The 6, 12 and 4 ohm resistors are in parallel resulting in 2 ohms. As a result, this is in series with the 2 ohm resistors. I can't seem to find where the error is?

 

[robphy]

You wrote

Step 2: the 2 ohm resistor and the 3 ohm resistor are in series, which results to 4 ohm.

It's a 2-ohm in series with the equivalent-2-ohm, yielding 4-ohms.

 

[sugz]

You wroteIt's a 2-ohm in series with the equivalent-2-ohm, yielding 4-ohms.

Sorry about that. I must have made a mistake with that. Thanks for pointing that out!