An ideal battery sends a current of \( 6 \) A in a resistor \( R \). On connecting an additional resistor of value \( 12\,\Omega \) in parallel to \( R \), the current through the battery is increased to \( 8 \) A. The resistance of resistor \( R \) will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 4\,\Omega \)
An ideal battery has no internal resistance, so its terminal voltage V stays the same when the second resistor is added. The extra current is simply the current through the new 12 Ω resistor.
\( V = 6R \quad \text{(before)} \)
\( I_{12} = 8 - 6 = 2\,\mathrm{A} \quad \text{(current through the } 12\,\Omega \text{ resistor)} \)
\( V = I_{12}\times12 = 2\times12 = 24\,\mathrm{V} \)
\( R = V/6 = 24/6 = 4\,\Omega \)
Check: \( R_{\mathrm{eq}} = (4\times12)/(4+12) = 3\,\Omega \) and \( 24/3 = 8\,\mathrm{A} \).