Question

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

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

Answer 1

Answer: (A), (B)

The maximum voltage range is obtained when all the components are connected in series

Explanation for correct options(A) and option(B).

The explanation for option(A):

The range of voltmeter $V$ is given by the expression

$\mathit{V}\mathbf{}\mathbf{=}{\mathit{I}}_{\mathbf{g}}\left(R_c+(R_c+R+R)\right)$

V is maximum in this case.

Thus option(A) is correct.

Explanation for option(B):

The range of ammeter I is given by the expression.

$I=\frac{I_g{R}_c}{R_{eq}}+I_g$

Where,

$\frac{1}{R_{eq}}=\frac{1}{R_c}+\frac{1}{R}$

Here $R_{eq}$​ is the minimum and therefore I is the maximum.

Thus option(b) is correct.

Explanation for incorrect options(C) and option(D).

Explanation for option(C):

The maximum current range is obtained when all the components are connected in parallel.

Thus option (c) is not the correct answer.

Explanation for option(D):

The maximum voltage range is obtained when all the components are connected in series.

Thus option (D) is not the correct answer.

Therefore the correct options are option(A) and option(B).