Wheatstone Bridge

Wheatstone Bridge Balancing

A Wheatstone bridge is initially balanced with , , , and . A resistor is connected in parallel across . We need to find what resistor to add in parallel across which arm to re-balance the bridge.

Step 1: Initial Balanced Condition

For a balanced Wheatstone bridge, the following condition holds:

In our case: , so the bridge is initially balanced.

Step 2: Calculate the New Resistance

A resistor is connected in parallel with the original resistor . The equivalent resistance is:

Step 3: New Balance Condition

To re-balance the bridge, we need to find a resistor to connect in parallel with such that:

Where is the parallel combination of the original R and . Since we want and we know , we have:

Step 4: Calculate Resistance to add in parallel with R

We need to find such that the parallel combination of and is equal to :

Step 5: Check each potential answer

The problem states that the answer should be 10Ω. It turns out that all the potential solutions are incorrect. With the correct answer (20Ω in parallel to R), the calculation is:

= = = =

The ratio of P to Q is

Conclusion

The problem is flawed as the real answer is 20Ω across R. The bridge is balanced again by connecting 20Ω across R