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

Question

Consider two identical galvanometers and two identical resistors with resistance R. If the internal resistance of the galvanometers R _ c is(are) true ?

Quantrex Academy · Accepted Answer

Correct answer: 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

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

Consider two identical galvanometers and two identical resistors...

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