Series RL circuit

A series resistance R and self-inductance L is driven by an input voltage . The output voltage across the inductor is measured by a very high impedance device which consequently draws negligible current from the circuit. Use the complex number method to calculate the current I in the circuit and the voltage across the inductor. So think of the input voltage as the real part of .

1. Show that the complex number representation of the current is:

   

   

   SOLUTION:
   

   We use to represent the complex number version of the real V.
   

   

   

   

   

2. The complex number representation of the output voltage will be the current times the complex impedance of the inductor. Hence show that:

   

   SOLUTION:
   

   Using :

   

3. Show that the actual voltage across the inductor is:

   

   (Remember .)
   

   SOLUTION:
   

   The actual voltage is :

   

   

   Hence the result.
   

4. What are the filter properties of this circuit? i.e. is it highpass, lowpass etc.

   SOLUTION:
   

   

   Hence it is a highpass filter.