Inductor and Capacitor at different frequencies

[tomrja]

Homework Statement

When a particular inductor and capacitor are connected across the same AC voltage, the current in the inductor is higher than in the capacitor. Is this true for all frequencies?

Homework Equations

Current through a capacitor Ip=(Vp)(2pi)(f)(C)

Current through an inductor Ip=(Vp)/((2pi)(f)(L))

The Attempt at a Solution

I know that the formula for the current in a capacitor is Ip=(Vp)(2pi)(f)(C) and the current through an inductor is Ip=(Vp)/((2pi)(f)(L)). So, to me it looks like the current through the capacitor would be larger than the current through the inductor at a given frequency, but the question itself states otherwise.

Thank you for your help!

 

[soothsayer]

So, to me it looks like the current through the capacitor would be larger than the current through the inductor at a given frequency, but the question itself states otherwise.

Not true at all, set up the ratio of current through the inductor (I_L) to current through the capacitor I_C and ask yourself what sort of inequality must be satisfied for I_L>I_C. You'll see it's quite reasonable. Remember, common capacitors and inductors have very tiny values in SI units. Next, ask yourself if there could be a frequency such that I_L<I_C