Can someone solve this !
pleae note that there's a figure containing following.

figure: rlc series circuit with resistance in parallel with the capacitor.

in the circuit the source delivers a sinusoidal output. for a particular frequency, the impedances are in the proportions of r : xc : xl is as 3 : 4 : 5.

r = 47 ω, l = 3.3 mh, c = 3.3 µf. the input provided by the source is e = 3.4 sin 1t v

a) calculate the voltages across and currents through the other components – including phase angles taking the emf from the source as reference.

b) calculate the (apparent) power input from the source and the power factor of the circuit.

All the calculations are shown in the explanation

Explanation:

RLC Circuit

The circuit proposed in the problem consists in one resistor R in series with the parallel of a capacitor C and an inductor L. All the impedances, voltages, currents and powers must be expressed as complex numbers since they all have an active and a reactive component. The formulas are very similar to those of the Ohm's law, as will be shown below.

The source has a time function expressed as

We must find the RMS voltage as

The given parameters of the circuit are

(a)

Let's find the reactances

Now the impedances are

The equivalent impedance of the parallel of the capacitor and the inductor is

Computing the total impedance of the circuit

Converting to phasor form

The given voltage of the source is

It has an angle of 0 degrees since it's the reference. Let's compute the total current of the circuit

We can see the current leads the voltage, so our circuit has a capacitive power factor, as shown ahead .

The voltage acrosss the resistor is

The currents through the capacitor and inductor will be computed with the formula of the current divider .

(b) The aparent power from the source is the product of the voltage by the total current

Finally, the power factor is

As mentioned before, since the current leads the voltage, the circuit is primarily capacitive

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y