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How would you solve a question based on an unbalanced Wheatstone bridge?

3 viewed last edited 3 years ago Anonymous
0

Using Kirchoff's loop rule is the way to go (I think)

The question is as follows

(Luckily found the question online) I keep getting the wrong answer. Mahesh Godavarti
1

Let's set up the equations appropriately.

Let I_i be the current through R_i . I will assume the currents flowing top to bottom and left to right.

Then we have:

24 = I_1 R_1 + I_4 R_4 = I_2 R_2 + I_5 R_5

I_1 R_1 + I_3 R_3 = I_2 R_2

I_1 = I_3 + I_4

I_5 = I_2 + I_3

We have five equations in five unknowns. Let's solve them!

24 = I_1 R_1 + R_4 (I_1 - I_3) = I_2 R_2 + R_5 (I_2 + I_3)

24 = I_2 (R_2 + R_5) + I_3 R_5

24 = I_2 R_2 - I_3 R_3 - R_4 I_3 + R_4 (I_2 R_2 - I_3 R_3 ) / R_1 \implies 24 = I_2 R_2 (1 + R_4 / R_1) - I_3 R_3 (1 + R_4 / R_1) \implies 24 R_1 / (R_1 + R_4) = I_2 R_2 + I_3 R_3

Therefore,

24 = 300 I_2 + 250 I_3

8 = 50 I_2 + 100 I_3

Therefore, I_3 = 24 / (350) A, I_2 = 12 / 75 = 4/ 25 A .

Solve, for the rest.