Circuits-equivalent resistance

[smoics]

circuits--equivalent resistance

Homework Statement

What is the equivalent resistance between points a and b in the figure ?

Homework Equations

Resistors in series add up, resistors in parallel are 1/(1/R + 1/R...)

The Attempt at a Solution

I tried 1/(1/16 + 1/12 + 1/4) + 5, but I get 7.5 and the answer is 7 ohms...where did I go astray?

 

[berkeman]

Homework Statement

What is the equivalent resistance between points a and b in the figure ?

Homework Equations

Resistors in series add up, resistors in parallel are 1/(1/R + 1/R...)

The Attempt at a Solution

I tried 1/(1/16 + 1/12 + 1/4) + 5, but I get 7.5 and the answer is 7 ohms...where did I go astray?

It's a 6 Ohm resistor in the figure, and 16 Ohms in your calculation...

 

[smoics]

Why wouldn't you add the 6+10=16? Because they're in series and the rest are in parallel...Yet when I add them all up as if they are in parallel, plus the "Extra" 5, I get the correct answer...

 

[berkeman]

Why wouldn't you add the 6+10=16? Because they're in series and the rest are in parallel...Yet when I add them all up as if they are in parallel, plus the "Extra" 5, I get the correct answer...

The 6, 12 and 4 Ohm resistors are in parallel. See how they all are connected at their tops with solid wire lines? And the same for their bottoms -- all connected with solid wire lines.

And as for the 10 Ohm resistor -- can you see how there is a solid wire line all the way from its top to its bottom? What is the parrallel combination of a resistor and a wire...?

 

[smoics]

So it takes the path of least resistance, which is NOT through the 10 ohm resistor?

 

[berkeman]

So it takes the path of least resistance, which is NOT through the 10 ohm resistor?

Correct-amundo. When you short out a resistor with a wire, you get zero Ohms (for ideal wire -- for real wire, it's still close to zero Ohms).


EDIT -- So do you get the right answer now?

 

[smoics]

Yes--merci beaucoup!