Why $u(t)$ and $i(t)$ are in the same phase in a resistor, but in a condensator $i(t)$ is ahead of $u(t)$ by $\pi/2$, and vice versa in a coil?

Note: I need physical explanation, like main reason of this act. No need for mathematical reasons like

$$ i(t) = C \frac{du}{dt} $$ When $u(t)=U\sqrt{2}\sin\omega t$, then $i(t)=C\omega\cdot U\sqrt{2}\sin(\omega t+\pi/2)$.

This case is for condensator as you know.

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    $\begingroup$ Welcome New contributor Physics009! What do you mean by 'physical explanation'? What research effort have you already done to find such an explanation? Should the reader assume that you have done zero research on the physical basis of resistance and capacitance? If you have done some research, it would be helpful if you share that and explain what remains unclear. You might find the following link helpul: How do I ask a good question? - "Have you thoroughly searched for an answer before asking your question?" $\endgroup$ – Alfred Centauri Sep 15 '19 at 12:56
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    $\begingroup$ Do you understand why the capacitor is described by $i(t)=c\frac{du}{dt}$? Because once you understand why the equation describes the behavior of the capacitor in time domain, you understand why the capacitor voltage lags current for AC excitation. $\endgroup$ – The Photon Sep 15 '19 at 15:55

In a resistor current flow directly causes a voltage drop so the voltage and current vary together with no lag: eg. if there is a step function of current there is a step function of voltage with no delay between the steps.

In a capacitor being supplied with a current, the current supplies the capacitor with a flow of electrons which it accumulates (integrates as a function of time) and the voltage across the capacitor is a function of its accumulated charge, or total charge. eg. if there is a step function of current there is a linear ramp function of voltage instead of a step function.

It is this integration, or accumulation, as a function of time that causes the phase difference between the voltages across the resistor and the capacitor. eg. if the current into the capacitor is a sine wave, the voltage on the capacitor will be a cosine wave--the integral of the sine wave. Hence the pi/2 lagging phase difference.

Similarly for an inductor except the integral becomes a derivative and the phase difference becomes leading.


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