Connecting RL Combination to Output Time Derivative of Input Voltage

[e_sovalye]

1-How could an RL combination be connected to produce an output voltage which is the time derivative of the input voltage?

2-Show that taking the time derivative of a sinusoidal function [such as cos(wt+a)] always has the effecton increasing its phase pi/2.

3-İf the internal series resistance of an inductor is not negligible , how will this change the relative phase of voltage and current fort he inductor?

 

[fargoth]

1. parallel connecet R to the input and parallel to the put L, the voltage on L is proportional to the derivative of the current which is proportional to the input voltage...
2. you know what the derivative of cos(wt+a)? what's the phase change between sin and cos?