Question

In the circuit shown in figure, a 12 V power supply with unknown internal resistance $r$ is connected to a battery with unknown emf $E$ and internal resistance 1$\Omega$ and to a resistance of 3$\Omega$ carrying a current of $2A$. The current through the rechargeable battery is $1A$ in the direction shown. Find the unknown current $i$, internal resistance $r$ and the emf $E$.

• A. $E=-5V$ and $r=2\Omega$
• B. $E=-7V$ and $r=3\Omega$
• C. $E=-9V$ and $r=2\Omega$
• D. $E=-5V$ and $r=5\Omega$

Answer 1

The correct option is A $E=-5V$ and $r=2\Omega$

Applying loop law equation in upper loop we have,

$E+12-ir-1=0$ (i)

Applying loop law equation in lower loop we have

where

$i=1+2=3A$

$E+6-1=0$ (ii)

Solving these two equations we get,

$E=-5V$ and $r=2\Omega$