A Wheatstone bridge is most sensitive when

A. The ratio arm is equal to one

In a Wheatstone bridge, the sensitivity refers to how easily you can detect a change in the unknown resistance. For maximum sensitivity, a specific condition on the ratio arms is required:

A. The ratio arm (one of the known resistances) is close in value to the unknown resistance.

Here’s why:

• The Wheatstone bridge works by balancing the potential difference across a galvanometer.
• When all resistors have similar values, even a small change in the unknown resistance will cause a more significant deflection in the galvanometer compared to a situation where the ratio arm is much larger or smaller than the unknown resistance.

So, option A is the most accurate statement.

Here’s why the other options are not quite true:

• B. The ratio arm is equal to ten: While having the ratio arm close in value is important, an exact match of 10 isn’t necessary. It should be in the same order of magnitude as the unknown resistance for optimal sensitivity.
• C. Any value: Not any value will provide maximum sensitivity. As explained above, a ratio arm close to the unknown resistance is crucial.
• D. Both a and b are true: While option A captures the essence of sensitivity, option B is not entirely accurate as mentioned above.