A cell of emf E and internal resistance r gives current of 0.5 A with external resistance of $12 \Omega$ and a current of 0.25 A with an external resistance $25 \Omega$. What is the value of internal resistance?

$1 \Omega$

The correct answer is Option (2) → $1 \Omega$

According to Ohm's law,

$V=IR$

Case I: $V=E, I=0.5A$ and $R=12Ω$

$∴E=0.5(12+r)$

Case II: $V=E, I=0.25A$ and $R=25Ω$

$∴E=0.25(25+r)$

$⇒0.5(12+r)=0.25(25+r)$

$=24+2r=25+r$

$r=1Ω$