In the circuit shown in the figure, \( P \neq R \). The reading of the galvanometer remains the same with switch \( S \) open or closed. Then
Show Hint
In circuits with multiple branches and switches, if the reading of the galvanometer remains unchanged with the switch in different positions, it indicates that the current through the galvanometer is independent of the switch position and equal to the current in a specific branch.
Step 1: Understanding the Question:
If the reading of the galvanometer \( I_G \) does not change when the switch \( S \) is closed, it means that no current flows through the switch \( S \). This indicates that the points connected by the switch are at the same potential. Step 2: Key Formula or Approach:
This is a property of Kelvin's method for measuring the resistance of a galvanometer. For the bridge to be balanced such that no current flows through the switch branch, the ratio of resistances must be consistent. Step 3: Detailed Explanation:
In this specific bridge configuration, if closing the switch does not affect the galvanometer current, the potential at point B must equal the potential at point D.
This balance condition implies that the current \( I_Q \) flowing through the top right resistor must continue directly into the galvanometer branch because there is no diversion of current at the junction B toward S.
Therefore, in this balanced state, the current through arm Q is the same as the current through the galvanometer branch G.
So, \( I_Q = I_G \). Step 4: Final Answer:
The correct relation is \( I_Q = I_G \).
