(i) State the principle of working of a meter bridge.
(ii) In a meter bridge balance point is found at a distance `I_(1)` with resistances R and S as shown in the figure. When an unknown resistance X is connected in parallel with the resistance S, the balance point shifts to a distance `I_(2)`. Find the expression for X in terms of `l_(1), l_(2)` and S.

Explanation

### Solution:

**(i) Principle of Working of a Meter Bridge:**

The meter bridge operates on the principle of the Wheatstone bridge. It consists of a one-meter-long uniform wire that is used to compare two resistances. When a current passes through the wire, a jockey is used to find a point along the wire where the galvanometer shows no deflection (null point). At this point, the ratio of the resistances on either side of the bridge is equal to the ratio of the lengths of the wire on either side of the jockey.

Mathematically, if R is the known resistance and S is the unknown resistance, and L1 is the length of the wire on the side of R and (100 - L1) is the length on the side of S, then:

...