Question

N identical voltage sources of emf E each and internal resistance r and N identical resistors each of resistance R form a closed circuit as shown in the figure. The potential difference between the point A and B dividing the circuit into n and N-n units will be

• A. $NE$
• B. $(N-n)E$
• C. $nE$
• D. $0$

Answer 1

Answer: (D)

$0$

All the sources are aligned in the same direction, so the effective emf adds up.

Effective emf $=N\times E$

Effective resistance $=Nr+NR$ .

current($i$) $=\frac{NE}{N(r+R)}$

$=\frac{E}{r+R}$

The voltage across n units $=n(E-i(r+R\left)\right)$

$=0$