Question

A 20 ohm resistive element, a coil of L = 100 millihennries and a capacitor of 5 uF capacitance are connected in series to form an RLC branch.

A voltage v(t) = 7*311.12*sine(377t) volts is applied to the RLC branch.

It is requested:

1. The numerical value of Z_RLC
2. Write the expression for i(t), using numerical coefficients.
3. Write the expression for p (t), using numerical coefficients, and express all trigonometric functions with exponents not greater than unity.
4. The average value of the power delivered to the branch.
5. Find and graph v_R(t), v_L(t), v_C(t), i(t) y p(t).

Answer 1

Ans)

a)

Given input voltage

in phasor form

frequency comparing with sin(wt) is

now impedance is

answer in both rectangular and polar form if you want only magnitude i.w mag(Z)=493.21 ohms

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b)

Current is given as

now in time domain it is

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c)

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d)

many ways to calculate average power simplest way is by knowing the fact the only resistor is absorbing the power ,average power is simply power dissipated in resistor

4.416 is peak value of current obtained above

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e)

now time domian expression is

Now plots are