Question: 38: A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q
(1) should be very large and unequal
(2) do not play any significant role
(3) should be approximately equal to 2 X
(4) should be approximately equal and are small
Answer: Option (4)
Explanation:
In a Wheatstone bridge, the condition for balance is given by \frac{P}{Q} = \frac{X}{Y}.
Under this condition, no current flows through the galvanometer,
and the value of the unknown resistance X can be determined accurately.
The precision of measurement depends on the sensitivity of the galvanometer,
which is maximum when a small change in X
produces a noticeable deflection in the galvanometer.
This sensitivity is highest when the ratio arms P and Q
are approximately equal, that is P \approx Q.
Also, for greater current in the bridge and hence better galvanometer sensitivity,
the resistances P and Q should be small.
Therefore, for the most precise measurement of the unknown resistance X,
the resistances P and Q should be approximately equal and small.
Hence, the correct answer is Option (4).