Observe the circuit:

The input sine voltage is .

Compare the function with .

Here .

,  and are in parallel.

The total impedance is

(b)

The input sine voltage is .

Compare the function with .

in polar form can be written as .

The sine voltage can be written as .

From (a):

can be written in polar form is .

Find the total current.

Total current is

(c)

From (b):

The input sine voltage in polar form is .

Resistor .

Find the total current across the resistor.

Total current is 

can be written in complex form is

(d)

From (b):

The input sine voltage in polar form is .

Capacitor .

Capacitor voltage lags capacitor current by .

 in polar form is

Find the total current across the capacitor.

Current across the capacitor is .

 can be written in complex form is

(e)

From (b):

The input sine voltage in polar form is .

Inductance .

Inductor current lags inductor voltage by

in polar form is

Find the total current across the inductor.

Current across the inductor is 

can be written in complex form is