Deriving a balanced bridge equation

  • Thread starter quaker
  • Start date
  • #1
quaker
14
0
I am having trouble finishing this problem. I am supposed to first derive an equation for V_5 in this circuit:

http://img292.imageshack.us/img292/599/picture3qy2.png [Broken]

I applied a Delta-Wye transformation to get here:

http://img292.imageshack.us/img292/9672/workot8.jpg [Broken]

From there I am supposed to show that the circuit is balanced when R1/R2 = R3/R4 for any value of R5. This is where I'm getting stuck. My attempt starts by setting the V5 equation equal to zero and then trying to reduce it. This isn't working very well since the V5 equation is pretty messy to begin with.

Am I going about this correctly, or is there an easier method I should use? Thanks for your help.
 
Last edited by a moderator:

Answers and Replies

  • #2
doodle
161
0
Yes, I think the V5 equation is messy. But there's an easier way to show the condition for a balanced bridge.

The bridge is balanced if V2 = V4 since there will be no current then across R5. This also means V1 = V3. Then, from applying Ohm's law to the 2 equations and canceling the currents, you should get R1/R2 = R3/R4 quite easily.
 

Suggested for: Deriving a balanced bridge equation

  • Last Post
Replies
5
Views
532
Replies
2
Views
398
Replies
16
Views
2K
  • Last Post
Replies
3
Views
469
  • Last Post
Replies
8
Views
1K
Replies
35
Views
1K
  • Last Post
Replies
17
Views
3K
Replies
10
Views
2K
Replies
0
Views
343
  • Last Post
Replies
5
Views
1K
Top