1. Condition at resonance in a series LCR circuit

   For a series LCR circuit, the impedance is $Z = \sqrt{R^2 + (X_L - X_C)^2}$

   At resonance, $X_L = X_C$ so the impedance becomes minimum: $Z = R$

2. Current amplitude at resonance

   If the source emf amplitude is $E$, then current amplitude at resonance is $I = \frac{E}{R}$

   Initially, this is given as $I_0$, so $I_0 = \frac{E}{R}$

3. When resistance is doubled

   New resistance: $R' = 2R$

   At resonance, the new current amplitude is $I' = \frac{E}{R'} = \frac{E}{2R}$

   Using $I_0 = \frac{E}{R}$, $I' = \frac{1}{2} \cdot \frac{E}{R} = \frac{I_0}{2}$

4. Option check

   • A: $\frac{I_0}{2}$ ✅
   • B: $\frac{I_0}{\sqrt{2}}$ ❌
   • C: $2I_0$ ❌
   • D: $I_0$ ❌

Therefore, the correct answer is A.