Solving a Complex Kirchoff's Law Problem - Mike's Request for Help

[physicsfun_12]

Homework Statement

Hello there, hope you are well.

I am having trouble solving this problem involving Kirchoff's laws.

I have attached a copy of the circuit and problem to this post in jpeg format.

Thanks again in advance for any help.

Mike

Homework Equations

The Attempt at a Solution

Well I merged to the two 20 ohms into one 10ohm and said that the total voltage in any loop equals zero.

so 60=20Ia + 10Ib

and 20=20Ib + 10Ia

I have tried solving this many times and keep getting a negative current for Ib. My original equation must be wrong.

Thanks a lot for any help or input,

Mike

 

[tiny-tim]

Hi Mike!

… 60=20Ia + 10Ib

and 20=20Ib + 10Ia

Which loop has Ia, and which has Ib, and in which direction?

And what about Ic ?

(and where do those 20s on the RHS come from?)

 

[physicsfun_12]

I think I've got it now.

I was using loop analysis so that's why there is only two currents.

The 20s came from 60=10Ia + 10(Ia+Ib) which expands to give 20Ia + 10Ib

You can work out the currents using simultaneous equations, giving a Ia=3.333A and Ib=-0.6666A

I of the load resistor, Il=Ia+Ib = 2.6667A

So Vl=2.6667*10 = 26.667V

Does this look about right? Thanks a lot for your help

Mike

 

[tiny-tim]

The 20s came from 60=10Ia + 10(Ia+Ib) which expands to give 20Ia + 10Ib

ohhh! you should always state an intermediate step like that

(apart from anything else, you stand a good chance of making a mistake with ±s if you don't write this stuff out clearly)

Yes, the answer looks ok now.

 

[physicsfun_12]

Sorry about that, you are absolutely right... that's most probably why I was getting it wrong in the first place!

Thanks for your help and take care,

Mike