Is the Calculation of Req Correct in This Circuit Problem?

[Mach]

Homework Statement

Calculate i2, given that r1=12, r2=6, r3=12, r4=6.
There is a 20V source.

The first step here is calculate Req, I believe.

http://media.newschoolers.com/uploads/cache/images/1222468444-632813-600x325-1222468266Untitled2423423.jpg

Homework Equations

Req=(r1 ll r2) + (r3 ll r4)

note: ' ll ' means parallel.

The Attempt at a Solution

1/Req = 1/(6+12)+1/(6+12)

Req=9

The answer says that Req should be 8. Is my formula for Req correct?

 

[hage567]

I think you have the right idea but you're getting the math wrong.

For two resistors in parallel, the equivalent resistance is \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}

This is NOT the same as \frac{1}{R_{eq}} = \frac{1}{(R_1+R_2)}! (which is what you have done.)

So take it one step at a time, and solve for the Req of R1 and R2, then for R3 and R4, then the Req of the circuit.

 

[The Electrician]

Imagine that you remove the wire carrying I2. Assume that the negative side of the voltage source is taken to be a reference (ground). What is the voltage at the junction of R1 and R3? What is the voltage at the junction of R2 and R4? I think that if you calculate those two voltages, you will see that it doesn't take much more calculation to determine I2.

 

[Mach]

Thanks a lot! I got the answer and have a better understanding of circuits!

By the way thanks for not giving me the answer, haha.

For those others trying the question the answer is: i2=0.833A

 

[The Electrician]

Be careful. It looks to me like if you remove the wire carrying I2, the voltage at the junction of R1 and R3 will be 10 volts (with respect to the negative end of the voltage source), and the voltage at the junction of R2 and R4 will also be 10 volts. Do you agree?

And, if that's the case, what will be the value of I2?