Final answer:
When the peak EMF voltage across a capacitor is doubled at the same frequency, the peak current through it also doubles. Thus, the new peak current would be 20.0 mA.
Step-by-step explanation:
The peak current through a capacitor is directly proportional to the peak emf (electromotive force) across it. When the peak emf voltage is doubled while maintaining the original frequency, the peak current through the capacitor will also double, according to the capacitive reactance formula I_peak = V_peak / X_C, where X_C is the capacitive reactance and is not changed because the frequency is constant. Therefore, if the peak current was originally 10.0 mA and the peak voltage is doubled, the new peak current would be 20.0 mA.