The relationship DV = IR applies for resistors in an AC circuit, so the current is:

I(t)

=

Vo R

sin(wt)

What happens to the peak current when the frequency of the voltage is increased?

1. Increasing f would increase the peak current
2. Increasing f would not affect the peak current
3. Increasing f would decrease the peak current

The peak current is just the peak voltage over the resistance, and does not depend on frequency. In addition, the current is in phase with the voltage.