Question

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

• A. \( I_Q = I_G \)
• B. \( I_Q = I_R \)
• C. \( I_R = I_G \)
• D. \( I_P = I_G \)

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.

Answer 1

The Correct Option is D

Step 1: Understanding the circuit.
We are given a circuit with a galvanometer \( G \), and there are multiple branches and components, including resistors \( P \), \( R \), and \( Q \). The problem states that the reading of the galvanometer remains the same when switch \( S \) is open or closed, meaning that there is no change in the current measured by the galvanometer regardless of the switch position.
We need to determine the relationship between the currents in the various parts of the circuit, specifically the current \( I_P \), which is the current through the resistor \( P \), and the current \( I_G \), which is the current through the galvanometer.

Step 2: Analyzing the circuit with switch \( S \) open.
When switch \( S \) is open, the current \( I_P \) flows through the resistor \( P \), and the current splits between resistors \( Q \) and \( R \). Since the current through the galvanometer remains constant, we infer that the current through the branch containing the galvanometer must not be influenced by the switch position. This means that the current \( I_P \) must be equal to the current through the galvanometer \( I_G \) when the switch is open.

Step 3: Analyzing the circuit with switch \( S \) closed.
When switch \( S \) is closed, the current now flows through the additional path that includes the switch. However, the problem states that the reading of the galvanometer does not change, which suggests that the current flowing through the galvanometer still remains unchanged. This implies that the current \( I_P \), the current through the resistor \( P \), must still be equal to \( I_G \), as there is no alteration in the current through the galvanometer.

Step 4: Conclusion from circuit behavior.
Given that the reading of the galvanometer remains unchanged regardless of whether switch \( S \) is open or closed, the current through the galvanometer, \( I_G \), must be equal to the current through the resistor \( P \), denoted by \( I_P \).
Final Answer:
Thus, the correct relationship is:
\[ \boxed{I_P = I_G}. \]