A) \[\ell \]
B) \[2\ell \]
C) \[\ell /2\]
D) \[\ell /4\]
Correct Answer: C
Solution :
| [c] Balancing length \[l\] will give emf of cell |
| \[\therefore \]\[E=Kl\] |
| Here K is potential gradient. |
| If the cell is short circuited by resistance R' |
| Let balancing length obtained be V then\[V=kl'\] |
| \[r=\left( \frac{E-V}{V} \right)R\] |
| \[\Rightarrow \]\[V=E-V\] \[[\because r=R\,\text{given}]\] |
| \[\Rightarrow \]\[V=E-V\]\[\Rightarrow \]\[2V=E\]or\[2Kl'=Kl\] |
| \[\therefore \]\[l'=\frac{l}{2}\] |
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