Question

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:

• A. Should be approximately equal to 2X
• B. Should be approximately equal and are small
• C. Should be very large and unequal
• D. Do not play any significant role

Answer 1

The Correct Option is B

In a Wheatstone bridge, the principle of operation relies on the precise balancing of two ratios of resistances. The bridge is balanced when the ratio of two known resistances (P and Q) equals the ratio of unknown resistance (X) and variable resistance (Y). Mathematically, this can be expressed as:

\(\frac PQ = \frac XY\)

In order to ensure the most precise measurement of the unknown resistance X, the resistances P and Q should have certain properties. Ideally, for optimal sensitivity and accuracy:

• Equal: P and Q should be approximately equal. This minimizes the impact of any measurement errors and balances the bridge with the greatest sensitivity.
• Small: P and Q should be small in value. Lower resistances reduce the effect of any non-ideal factors such as the resistance of connecting wires and contact resistances, improving accuracy and precision.

In conclusion, for precise measurement, the resistances P and Q "Should be approximately equal and are small." This ensures the Wheatstone bridge operates under optimal conditions, minimizing potential errors.