1. The problem statement, all variables and given/known data
An AC voltmeter connected to the nodes A and B shows the same value as when connected to the nodes A and D (refer to attachment). What is the inductance of the inductor? What value does the voltmeter show? The inductor is ideal. U = 70sin(314t) V, C = 80 μF, R = 500 Ω.
2. Relevant equations
[itex] U_{rms} = \frac{U_{max}}{\sqrt{2}}[/itex]
[itex] Z_L = i \omega L; Z_C = -\frac{i}{\omega C} [/itex]
[itex] \omega = \frac{1}{\sqrt{LC}}[/itex]
3. The attempt at a solution
For the voltages to be equal, the voltage drop across the inductor and capacitor in parallel should be 0. I know that in the case of series resonance, the voltage drop across the inductor and the capacitor is 0. Although here we also have a capacitor in parallel of the inductor, and due to the parallel resonance the voltage across these two elements is maximum (infinite). So what is confusing me, is that what is the actual voltage drop when we have simultaneous resonances? Could we say that the across the capacitor in series it is -∞ V, across the inductor ∞ V, thus resulting in 0 V in total (in series)?
An AC voltmeter connected to the nodes A and B shows the same value as when connected to the nodes A and D (refer to attachment). What is the inductance of the inductor? What value does the voltmeter show? The inductor is ideal. U = 70sin(314t) V, C = 80 μF, R = 500 Ω.
2. Relevant equations
[itex] U_{rms} = \frac{U_{max}}{\sqrt{2}}[/itex]
[itex] Z_L = i \omega L; Z_C = -\frac{i}{\omega C} [/itex]
[itex] \omega = \frac{1}{\sqrt{LC}}[/itex]
3. The attempt at a solution
For the voltages to be equal, the voltage drop across the inductor and capacitor in parallel should be 0. I know that in the case of series resonance, the voltage drop across the inductor and the capacitor is 0. Although here we also have a capacitor in parallel of the inductor, and due to the parallel resonance the voltage across these two elements is maximum (infinite). So what is confusing me, is that what is the actual voltage drop when we have simultaneous resonances? Could we say that the across the capacitor in series it is -∞ V, across the inductor ∞ V, thus resulting in 0 V in total (in series)?
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