If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# LC natural response derivation 3

We use Euler's Formula to change our complex exponential solution into a solution expressed in terms of sines and cosines. Created by Willy McAllister.

## Want to join the conversation?

• What does Phasor notation have to do with Euler's?
• Euler's equation says we can disassemble a sine or cosine into the sum of two complex exponential terms. We do this disassembly because it is simpler to solve a circuit with exponential inputs compared to sine or cosine inputs. The word phasor refers to the exponential term, specifically when there is a phase shift represented by angle phi: e^j(wt + phi) = e^jwt * e^jphi. We call the term e^jphi a Phasor.
• do i need to constantly come up with a solution or do i just use the solution presented in this video? Or does it vary?
(1 vote)
• The solution for LC Natural Response is derived independent of the value of L and C, so it is a general solution for the circuit LC configuration presented. Likewise with the RC and RL Natural Responses.

The next more complex circuit is R L and C together. You start again from scratch to derive the general solution(s) for that new circuit. The RLC solution is quite rich and varied. I consider it the "Queen of Analog Circuits" with wide application to most analog systems.

Anything more complex than RLC is best viewed as a "filter". We don't use the same solution method as for simpler circuits, but rather move on/up to Laplace Transform Theory.