What is the resonant frequency and peak current drawn

[Perodamh]

Homework Statement

A series RLC current having a resistance of 40ohms and inductance of 400mH and a capacitance of 300microfarad is energized from 50Hz, 200V A.C supply. Find
i) Resonance Frequency of the circuit
ii) Peak current drawn by the circuit at 50Hz
iii) Peak current drawn by the circuit at resonance frequency.

Homework Equations

Resonance frequency: 1/2pi * sqrt (L* C), where L is the inductance and C capictance
the formula for peak current, I'm not so sure I₀ = vpeak/ z (impedance)

The Attempt at a Solution

for the first solution
Resonance frequency = 1/2pi * sqrt (L* C)
L = 400mH
C= 300microfarad
=1/6.28 * Sqrt ((400/1000) * (300*10^-8) )
=0.3263 * 10^-3

for the second and third solution I'm not sure how to use the formula and if it applies to this particular question. I don't mind being referred to any pdf file that covers A.c circuit analysis well and could help me solve this, or maybe the right formula and I could try solve the problem.

 

[gneill]

Microfarads are 10^-6, not 10^-8.

the formula for peak current, I'm not so sure I₀ = vpeak/ z (impedance)

Yes, but that will give you a complex value (a phasor, actually). You'll want its magnitude, which will give you the instantaneous peak current.

 

[BvU]

Hello Perodamh,

Resonance frequency: 1/2pi * sqrt (L* C)

Check the dimension !
Your equation lacks some brackets !

There is some material here , here , and even a calculator here to check your result.
I like the text https://www.electronics-tutorials.ws/accircuits/series-circuit.html
and the resonance frequency formula https://www.electronics-tutorials.ws/accircuits/series-resonance.html

 

[Perodamh]

Thanks, i'd try and let you know what I came up with

Hello Perodamh,

Check the dimension !
Your equation lacks some brackets !

There is some material here , here , and even a calculator here to check your result.
I like the text https://www.electronics-tutorials.ws/accircuits/series-circuit.html
and the resonance frequency formula https://www.electronics-tutorials.ws/accircuits/series-resonance.html

Microfarads are 10^-6, not 10^-8.

Yes, but that will give you a complex value (a phasor, actually). You'll want its magnitude, which will give you the instantaneous peak current.