Question

When a resistance of $2ohm$ is connected across the terminals of a cell, the current is $0.5amp$. When the resistance is increased to $5ohm$, the current is $0.25amp$. The emf of the cell is:

• A. $1.0$ volt
• B. $2.0$ volt
• C. $1.5$ volt
• D. $2.5$ volt

Answer 1

The correct option is C $1.5$ volt

emf$=I(R+r)-----\left(a\right)$

When $I=0.5,R=2ohm$

we know that$,$

$emf=V$

Therefore $,Eq\left(a\right)$become $V=0.5(2+r)=>1/2(2+r)$

$2V=2+r$ ----------------------$\left(1\right)$

When $I=0.25,R=5ohm$

Therefore $Eq\left(a\right)$become

$V=0.25(5+r)$

$=>1/4(5+r)$

$4V=5+r$---------------------$\left(2\right)$

Subtract $eq\left(1\right)$ from $\left(2\right)$

$4V-2V=5+r-2-r$

$2V=3$

$V=3/2$

$V=1.5v$

Hence,

option $\left(C\right)$ is correct answer.