$\pi/2$ phase shift in RC circuit I just recently learnt Alternating Current and RCL circuits and I also learnt about phasers and various graphs. Now I also know that current lags in an LR circuit. My intuitive understanding of this is according to Lenz Law, the inductor will oppose the current and hence slow it down. So the current lags. But I wanted to know if there is any similar logic for a RC circuit. The capacitor doesn't seem to make the current lead by a phase difference of $\pi/2$. I have already studied the mathematical proof and everything works, but I wanted to have an intuitive understanding of both. 
 A: When a resistance $R$ is put in series with some other impedance $Z$, by Ohms law you have $U=(R+Z)\cdot I$, or 
$$I=U\cdot \tfrac{1}{R+Z}=U\cdot \tfrac{1}{R+Z}\tfrac{\overline{R+Z}}{\overline{R+Z}}=U\cdot \tfrac{(R+\mathbb{Re}(Z))-i\ \mathbb{Im}(Z)}{|R+Z|^2}.$$ 
If $Z$ has an imaginary part, then $I$ and $U$ differ by some phase. And yes, this is the case wether $Z$ comes from an inductance $Z_L$ or a capacitance $Z_C$.
On a macroscopic level, the inductance of an AC system is given by the impedance $Z_L=i\omega L$, where $i$ is the imaginary unit and both the frequency $\omega$ as well the inductance $L$ is some real, so $Z_L$ is purely imaginary and multiplication by $i$ corresponds to a rotation in the complex plane by $90°$ or $\tfrac{\pi}{2}$.
A capacitance gives the impedance $Z_C=\frac{1}{i\omega C}$, which you can re-write as $Z_C=-i\omega\left(\frac{1}{\omega^2 C}\right)$. So for a given input voltage frequency $\omega$, and a given circuit element with inductance $L$, you can design a capacitor circuit element with $Z_C=-Z_L$. Same goes in reverse- So these two passive impedances work similarly, and there is a phase shift too, albeit in the other rotating direction.
The behaviour of these circuit elements can be understood by considering the voltage law for circuits, which expresses energy conservation. If energy is stored by one circuit element (voltage drop at a resistor), it must go missing somewhere else. The different distribution of energy of an circuit with or without complex element make a difference in the current flow. The inductance voltage is, more microsopically motivated, given via $U_L=L\frac{\mathrm d}{\mathrm dt}I$ (relates to Lenz law), and described the reactive behaviour of the circuit element to current. The capacitance stores charges from the current and the relation is $U_C=\frac{1}{C}\int^t I \mathrm dt$. These two equations are the origin of $Z_L=i\omega L$ and $Z_C=\frac{1}{i\omega C}$ if you consider in a sinodial like current.
