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In the series configuration of the LC circuit, the inductor (L) and capacitor (C) are connected in series, as shown here. The total voltage V across the open terminals is simply the sum of the voltage across the inductor and the voltage across the capacitor.
A first order, low pass RC filter is simply an RC series circuit across the input, with the output taken across the capacitor. We assume that the output of the circuit is not connected, or connected only to high impedance, so that the current is the same in both R and C. The voltage across the capacitor is IXC = I/ÏC.