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Question No. 12
Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers Rc<R/2, which of the following statement(s) about any one of the galvanometers is(are) true?

(A) The maximum voltage range is obtained when all the components are connected in series
(B) The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer
(C) The maximum current range is obtained when all the components are connected in parallel
(D) The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors

Solution:

Key Concepts:

  • Voltage Range: To increase the voltage range, we need to connect components in series to share the voltage.

  • Current Range: To increase the current range, we need to connect components in parallel to share the current.

Given:

  • Two identical galvanometers each with internal resistance Rc (where Rc<R/2).

  • Two identical resistors each of resistance R.

For Maximum Voltage Range:

To protect a galvanometer from high voltage, we add series resistance. The maximum voltage range is achieved when the total resistance is maximized, so that for a given voltage, the current is minimized (within the galvanometer's limit).

  • Connecting all components (both galvanometers and both resistors) in series gives the highest total resistance: Rtotal=2Rc+2R.

  • This setup allows the galvanometer to handle the highest voltage without exceeding its current rating.

Thus, option (A) is true.
Option (B) suggests a mixed series-parallel connection, which would not maximize the total resistance as effectively as all in series. Hence, (B) is false.

For Maximum Current Range:

To protect a galvanometer from high current, we add shunt (parallel) resistance. The maximum current range is achieved when the equivalent parallel resistance is minimized, so that most current bypasses the galvanometer.

  • Connecting all components (both galvanometers and both resistors) in parallel gives the lowest equivalent resistance. The equivalent resistance of four parallel elements (each with resistance around R or Rc) is less than any individual resistance.

  • This setup allows the galvanometer to handle the highest total current while only a small fraction passes through it.

Thus, option (C) is true.
Option (D) suggests connecting galvanometers in series and then in parallel with resistors. This would not minimize the equivalent resistance as effectively as all in parallel. Hence, (D) is false.

Final Answer:

A and C

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