Question

A current of $I$ ampere flows through a resistance $R$ when connected across a cell of emf $E$ and internal resistance $1\Omega$. When $R$ is increased by $50\%$, the current through the circuit is $0.8A$. The value of $R$ is :

• A. $1\Omega$
• B. $1.5\Omega$
• C. $2\Omega$
• D. $4\Omega$

Answer 1

The correct option is A $1\Omega$

$I=\frac{E}{R+r}\Rightarrow I=\frac{E}{R+1}\Rightarrow E=R+1$
$0.8=\frac{E}{1.5R+1}\Rightarrow E=0.8(1.5R+1)=1.2R+0.8$
$1.2R+0.8=R+1\times 0.2R=0.2\times R=1\Omega$