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For this AC circuit it is known that $$\omega=10^4 \text{rad}/\text{s},L=0.1\text{H}$$ Find capacity of a capacitor, so that the effective value of current \$I\$ doesn't depend on resistance \$R\$. (Phase displacement doesn't change on \$R\$, we already know that).
My reasoning:
For as long as there is a \$U_{ab}\$ voltage, \$R\$ is going to affect current \$I\$, by Kirchhoff's law. If there is no a-b branch it's still going to affect it because \$U\$ is already fixed. So the only way is if there is no resistance on ab branch, that is if \$X_C=0\$, \$C=\infty\$.
Am I missing something?
Best Answer
There are only two ways that the current through a resistor can be independent of the value of the resistor:
The current is zero. This means that the applied voltage must be zero as well. Your solution of making the capacitance infinite (effectively a short circuit) falls into this category.
The resistor is connected to a current source. Here's a hint: The circuit as given shows a voltage source connected in series with an inductor, a Thévenin source. It can be redrawn as its Norton equivalent: a current source in parallel with that same inductor. This effectively puts the inductor in parallel with the capacitor and the resistor, too. Is there a way to make sure that all the current from the current source flows through only the resistor?