In series RC circuit , R=30ohm , C=0.25myuF , V=100V , and omega=100000rad/s1) find the current in the circuit?2)Calculate the voltage across R and C ?

3) Is the algebraic sum of these voltages more than the source voltage ? If yes , resolve the paradox?

1) The current at steady state, $I=\frac{{V}_{in}}{Z}=\frac{100}{50}=2A$

2) Voltage across the R, ${V}_{R}=IR=2\times 30=60V$

Voltage across the C, ${V}_{R}=\frac{I}{\omega C}=\frac{2}{100000\times 0.25\times {10}^{-6}}=80V$

3) The algebraic sum of them are indeed more than the total input. But these two voltages are out of phase. They are like two vectors mutually perpendicular to each other. The vector sum of these two vectors is $=\sqrt{{60}^{2}+{80}^{2}}=100V$

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