[Physics] Why is there a phase difference in RC circuit

capacitanceelectric-circuitselectric-currentelectrical-resistancevoltage

In a capacitor circuit,the there is 90 degree phase shift between current and voltage in capacitor(when supplied sinusoidalvoltage and it varies from 0 to 90 degrees in a RC circuit.Can somebody tell me why exactly there is a phase difference between 0 to 90 degrees in a RC circuit while a purely capacitive circuit has a phase difference of 90 degrees

Best Answer

This phenomenon can be explained by taking a look at the electrical impedance, which is caused by the R and C components. The electrical impedance $Z$ is composed as \begin{align} Z = R + i X \end{align} where $X$ is the reactance. This is for capacitors $X_C = -\frac{1}{\omega C}$ and for inductors $X_L = \omega L$. We can make a sketch of this in a complex plane, which looks like

source: wikipedia

Now you can see, that it depends on the ratio of $R$ and $X$ what the phase difference $\phi$ between the real electrical current ($R$ - direction) and the voltage ($Z$ - direction). The actual dependence being \begin{align} \varphi= \arctan{\left(\frac{X}{R}\right)} \, . \end{align} (in the electrical engineers notation with $j$ as the imaginary unit) From this you can also see that if you have nearly no electrical resistance $R$ you end up with a $90°$ phase difference.

I hope this answers your questions.

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