In the circuit shown, $V$ is a sinusoidal voltage source. The current $I$ is in phase with voltage $V$. The ratio of the amplitude of voltage across the capacitor to the amplitude of voltage across the resistor is ________.
An in-phase current means the series RLC impedance is purely real, so $\omega L=1/(\omega C)$. With $L=5$ H and $C=5$ F, $\omega=1/\sqrt{LC}=0.2$ rad/s.
The capacitor reactance is $X_C=1/(0.2\cdot5)=1\ \Omega$. The same current flows through capacitor and resistor, so their voltage-amplitude ratio is $X_C/R=1/5=$ **0.20**.
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