Question

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?

• 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

Answer 1

Answer: (A), (C)

$V _{\max }=2 I _{gmax}\left(2 R+\frac{ R _{ C }}{2}\right)$
$V _{\max }= I _{ gmax }\left(4 R + R _{C}\right)$

$I_{g \max } R_{c}=\left(I_{\max }-2 I_{g \max }\right) \frac{R}{2}$
$I_{g \max } R_{c}=\left(I_{\max } \frac{R}{2}-I_{g \max } R\right)$
$I_{g \max }\left(R_{c}+R\right)=I_{\max } \frac{R}{2}$
$I_{\max }=I_{g \max } \times \frac{\left(R_{C}+R\right)}{R / 2}$

$I _{\max }=I_{ g \max }\left(\frac{2 R _{ C }+\frac{ R }{2}}{\frac{ R }{2}}\right)$