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?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1\,\Omega \)
For a cell of emf \( E \) and internal resistance \( r \) connected to an external resistance \( R \), the current is \( I = E/(R + r) \), so \( E = I\,(R + r) \). The emf is the same in both cases, so the two products can be equated.
\( 0.5\,(12 + r) = 0.25\,(25 + r) \)
\( 6 + 0.5\,r = 6.25 + 0.25\,r \)
\( 0.25\,r = 0.25 \)
\( r = 1\,\Omega \)
Check: \( E = 0.5 \times 13 = 6.5\,\mathrm{V} \) and \( 0.25 \times 26 = 6.5\,\mathrm{V} \).