The current in a resistive series circuit is 7.0 A. On adding a resistance of \( 1.6\,\Omega \) in the same circuit in series, the current drops to 5.0 A. The original resistance of the circuit is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 4.0\,\Omega \)
The source voltage \( V \) is the same before and after, so by Ohm's law \( V = IR \) for the two cases. Resistances in series add.
\( \displaystyle 7R = 5\,(R + 1.6) \)
\( \displaystyle 7R = 5R + 8 \;\Rightarrow\; 2R = 8 \;\Rightarrow\; R = 4.0\,\Omega \)
Shortcut: Check by substituting an option: for \( R = 4\,\Omega \), \( V = 7\times4 = 28\,\mathrm{V} \) and the new current is \( 28/5.6 = 5.0\,\mathrm{A} \), as given.