A circuit contains an ideal battery, three resistors, and two ideal ammeters. The ammeters read 0.2 A and 0.3 A. After two of the resistors are switched, the readings of the ammeters did not change. Find the battery current

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

If $R_{2} = R_{1}, I_{1} = I_{2} = 0.15 A a n d I_{3} = 0.05 A$

If $R_{2} = R_{1},$ the battery current is I = 0.20 A

If $R_{2} = R_{3}, I_{2} = I_{3} = 0.1 A a n d I_{1} = 0.2 A$

If $R_{2} = R_{3},$ the battery current is I = 0.4 A

answer is A, C, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

As the ammeters are ideal, we can conclude that the three resistors $R_{1}, R_{2} a n d R$ are actually connected in parallel, the equivalent resistance being

$R_{e q} = \frac{R_{1} R_{2} R_{3}}{R_{1} R_{2} + R_{1} R_{3} + R_{2} R_{3}}$ In the figure, the electric currents on each resistor and battery are shown.

The readings of the two ammeters are different and, consequently, by simple symmetry considerations, resistors $R_{1} a n d R_{3}$ are necessarily different. In other words, if we interchange $R_{1} a n d R_{3},$ the readings of the ammeters will also be interchanged. Therefore, we have two possible alternatives.

$R_{2} = R_{1}$ (if resistors) $R_{2} a n d R_{1}$ switched, the readings of the ammeters do not vary) or $R_{2} = R_{3} (R_{2} a n d R_{3}$ can be switched and the ammeters do not change). The two solutions are: