Please answer all parts and write the equations clearly and explain... i am tryi

Question

Please answer all parts and write the equations clearly and explain... i am trying to understand physics... please don't just plug in the number

without showing what the general equation is from... thank you so much :D

(20%) Problem 2: An RLC series circuit has a 2.35 resistor, a 105 H inductor, and a 82.5 F capacitor 17% Part (a) Find the circuit's impedance, in ohms, at 130 Hz Grade Summary Deductions Potential 0% 100% sinO cosO cotan0 asinO acosO atan acotan sinh) 78 9 45 6 Submissions Attempts remaining: 20 % per attempt) detailed view coshOtanhO cotanh0 + 0 END Degrees O Radians BACKSPACE DELCLEAR Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback - 17% Part (b) Find the circuit's impedance, in ohms, at 2.5 kHz Hz? kHz? 17% Part (c) If the voltage source supplies an rms voltage of 552 V, what is the circuit's rms current in amperes, at a frequency of 130 17% Part (d) If the voltage source supplies an rms voltage of 552 V, what is the circuit's rms current, in amperes, at a frequency of 2.5 17% Part (e) what is the resonant frequency, in kilohertz, of the circuit? 17% Part (f) What is the rms current, Irms, in amperes, at resonance?

Explanation / Answer

a)

Impedance, Z = sqrt( R^2 + (2*pi*f*L - 1/(2*pi*f*C))^2 )

where f = 130 Hz,

L = inducance = 105 uH = 105*10^-6 H

C = capacitance = 82.5*10^-6 C

= sqrt(2.35^2 + (2*pi*130*105*10^-6 - 1/(2*pi*130*82.5*10^-6))^2 )

= 14.94 ohm <------ answer

b)

Impedance at f = 2.5 kHz

Z = sqrt(2.35^2 + (2*pi*2500*105*10^-6 - 1/(2*pi*2500*82.5*10^-6))^2 )

= 2.51 ohm <---------- answer

c)

Rms current = Vrms / Z = 5.52/14.94

= 0.369 A

d)

Rms current =  5.52/2.51

= 2.2 A

e)

At resonance, inductive reactance = capacitive reactance

Inductive reactance = 2*pi*fL

Capacitive reactance = 1/(2*pi*f*C)

So, for resonance , 2*pi*f*L = 1/(2*pi*f*C)

So, f = (1/sqrt(LC))/(2*pi)

= (1/sqrt(105*10^-6*82.5*10^-6))/(2*pi)

= 1710 Hz = 1.71 kHz

f)

At resonance,

Irms = Vrms/ R = 5.52/2.35 = 2.35 A <--------- At resonance, inductive reactance cancels out the capacitive reactance. So, only resistance remains in the impedance

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