Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A source of V rms has a frequency of Hz. At this frequency a pure coil and a pure capacitor each have a reactance of . Each is joined to the source in turn. The frequency is then raised to Hz, with the voltage unchanged. Find the current in the coil and in the capacitor at Hz. At what frequency does the capacitor draw A?
A pure coil has , and its current lags the voltage by . A pure capacitor has , and its current leads the voltage by . For both, and . Use henry and farad in the formulas.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. V. At Hz, , so each current is A.
Step 1. The coil at Hz. The frequency is times larger, so . The current is mA.
Step 2. The capacitor at Hz. Now . The current is A.
Step 3. The frequency for A. The reactance needed is . That is half of , so the frequency is twice Hz: Hz.
Answer: mA, A and Hz.
Check. The current in the coil fell from A to A, to an eighth. The current in the capacitor rose from A to A, to eight times.
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