Question

In a potentiometer of one- metre length, an unknown emf voltage source is balanced at $60 \,cm$ length of potentiometer wire, while a $3 \,V$ battery is balanced at $45 \,cm$ length. Then the emf of the unknown voltage source is

• A. 3 V
• B. 2.25 V
• C. 4 V
• D. 4.5 V

Answer 1

Answer: (C)

4 V

Answer 2

Let $l_{1}$ and $l_{2}$ be the balancing lengths with the cells $E_{1}$ and $E_{2}$ respectively, than $E_{1}=xl_{1}$ and $E_{2}=xl_{2}$
$\Rightarrow \frac{E_{1}}{E_{2}}=\frac{l_{1}}{l_{2}}$
or $\frac{E_{1}}{3}=\frac{60}{45}$
$\Rightarrow E=4\, V$