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Impedance- The ratio of a sinusoidal voltage to a sinusoidal current is called "impedance". 

 For a resistor:

when current, 
\[i = e^{j\omega t}\]
\[V = iR\]
\[V/i = R\]

So, the impedance of a resistor is = R


For a capacitor:

when voltage,
\[V = e^{j\omega t}\]
\[I = C\frac{dV}{dt}\]
\[\Rightarrow I = C j\omega e^{j\omega t}\]
\[\Rightarrow I = C j\omega V\]
\[\Rightarrow \frac{I}{V} = C j\omega \]
\[\Rightarrow \frac{V}{I} = \frac{1}{C j\omega} \]

So, the impedance of a capacitor is = \[\frac{1}{C j\omega} \]

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