Question

In the circuit shown in Figure. What must the emf $ϵ$ of the battery be in order for a current of $2.00A$ to flow through the $5.00V$ battery? Is the polarity of the battery correct as shown?

Answer 1

First, do series/parallel reduction. Now, apply Kirchhoff's laws and solve for $ϵ$.

$\Delta V_{adefa}=0$ or $-\left(20\Omega \right)\left(2A\right)5V-\left(20\Omega \right)I_2=0$ or $I_2=-2.25A$

$I_1+I_2=2A$ or $I_1=2A-(-2.25A)=4.25A$

$\Delta V_{adefa}=0$ or $\left(15\Omega \right)\left(4.25A\right)+ϵ-\left(20\Omega \right)(-2.25A)=0$

$ϵ=-108.75V$; polarity should be reversed.