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The current in an electrical circuit consisting of an inductor, resistor and capacitor in series with an alternating power source, is described by the equation

The exponentially decaying terms in the solution describe what is known as the transient current. The non-decaying terms describe the steady state current.
iii) Write down an expression for the steady state current for the solution in part
ii). Why would this expression remain unchanged if the initial conditions were different?
iv) Express the steady state current in the form R sin (20t + ), where R and are to be determined. Verify that, after only 1 second, the magnitude of the transient current is close to 1% of the steady state amplitude, R.

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