Question

The resistance of the rheostat shown in figure is $30\Omega$. Neglecting the ammeter resistance, the ratio of minimum and maximum current through the ammeter, as the rheostat is varied, will be:

• A. $\frac{2}{5}$
• B. $\frac{83}{15}$
• C. $\frac{9}{43}$
• D. $\frac{19}{43}$

Answer 1

The correct option is A $\frac{2}{5}$

Ref. image 1

The current in resistance in the middle of quadrilateral will be zero irrespective of rheostat position.

Therefore circuit will look like.

Ref. image 2

At first let rheostat have zero resistance

$\Rightarrow Req={(\frac{1}{30}+\frac{1}{60})}^{-1}=20\Omega$

Secondly let rheostat have $30\Omega$ resistance.

$\Rightarrow Req={(\frac{1}{30}+\frac{1}{60})}^{-1}+30=50\Omega$

$\Rightarrow \frac{I_1}{I_2}=\frac{20}{50}=\frac{2}{5}$

Therefore option A is correct.