Question

Find the potential difference between the points P and Q in the given circuit?

• A. 1V
• B. 1.55V
• C. 2.55V
• D. 1.33V

Answer 1

The correct option is B 1.55V

Cells are in parallel but mind the polarity of the cells and modify the formulae accordingly.
Cells are in parallel. We can use the direct formula. For two cells in parallel, we can apply
$E=\frac{E_1{r}_2+E_2{r}_1}{r_1+r_2}r=\frac{r_2{r}_1}{r_1+r_2}$
Let’s first find the equivalent cell for first two rows and then evaluate the equivalent combination considering the third.
For first two rows of cell it’s fairly simple as you just need to apply the above formula as it is.
Let’s do that:
$E=\frac{5\times 1+4\times 1}{1+1}E=4.5Vr=\frac{1}{1+1}=0.5\Omega$
Now this cell is again in parallel with the third given cell. But notice carefully that the third cell has the reverse polarity. Nothing to be scared of. You very well know that a “minus” sign is going to get things done pretty easily.
$E_{eq}=\frac{E{r}_3-E_{3}r}{r_3+r}=\frac{4.5\times 1-2\times 0.5}{1+0.5}=1.55V{r}_{eq}=\frac{r_{3}r}{r_3+r}=\frac{1\times 0.5}{1+0.5}=0.33\Omega$
So the potential difference is 1.55 V.