Answer
A.) $I_{R}=\frac{\epsilon_{0}}{R}$
B.)$I_{C}=\epsilon_{0} \omega C$
Work Step by Step
A.) Use a phasor-diagram analysis to find the expression for the peak current $I_{R}$
The voltage drop across the resistor is exactly in phase with the current through it.
B.) Find the expression for the peak current $I_{C}$
When a capacitor is in parallel with a resistor, there is no phase difference between the applied voltage and the voltage across both components
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