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JEE Advanced2016PhysicsCurrent ElectricityActual

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers R c < R 2 , which of the following statement(s) about any one of the galvanometers is(are) true ?

Options

  1. AThe maximum voltage range is obtained when all the components are connected in series
  2. BThe maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and
  3. CThe maximum current range is obtained when all the components are connected in parallel
  4. DThe maximum current range is obtained when the two galvanometers are connected in series and the combination i

Correct answer

B. The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and

Step-by-step solution

i = E 2 R + 2 R c V g 1 = i R c = E R c 2 R + R c = E R c 2 R + 2 R c i 2 = E 2 R + R c 2 V g 2 = i 2 2 × R c = 1 2 E 2 R + R c 2 × R c V g 2 = E R c 4 R + R c ....(2) Since R c R 2 2 R c R 2 R + 2 R c 3 R V g 1 > V g 2 i A = E R c Here i = E ( 2 R + 2 R c ) 2 R . 2 R c = E ( R + R c ) 2 R R c i B = 2 R 2 R + 2 R c × E ( R + R c ) 2 R R c = E 2 R c i A > i B

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