How Does Frequency Variation Affect Phasor Current in a Series Circuit?

[viciado123]

Impedance -- Current phasor

In a series circuit of two elements, the voltage and current, for w = 2000 rad/s, are V = 150|-45° and I = 4,74|-116,6°.That variation in the frequency of the source would result in a phasor current of 6 amps? Assuming an unlimited variation in the frequency, what is the maximum possible value for the current?


The answer is 23.6% reduction in f
And the maximum 15 amps


I not find the answer
My attempt:

Z = V/I = 31,6|71,6° = 9,97 + 30i
Xl = 30
wL = 30
L = 0,015 and f = 318Hz

For I = 6 amps I assumed I' = 6|-116,6
Z' = V/I' = 25|71,6° = 7,89 + 23,72i
Xl = 23,72
2pif'L = 23,72
f' = 252 Hz

I find f' reduction 20,76% is correct ? How I find the maximum value for the current ?

 

[vela]

In a series circuit of two elements, the voltage and current, for w = 2000 rad/s, are V = 150|-45° and I = 4,74|-116,6°.That variation in the frequency of the source would result in a phasor current of 6 amps? Assuming an unlimited variation in the frequency, what is the maximum possible value for the current?


The answer is 23.6% reduction in f
And the maximum 15 amps


I not find the answer
My attempt:

Z = V/I = 31,6|71,6° = 9,97 + 30i
Xl = 30
wL = 30
L = 0,015 and f = 318Hz

For I = 6 amps I assumed I' = 6|-116,6
Z' = V/I' = 25|71,6° = 7,89 + 23,72i
Xl = 23,72
2pif'L = 23,72
f' = 252 Hz

I find f' reduction 20,76% is correct ? How I find the maximum value for the current ?

Your mistake is in assuming the phase of the 6-amp current is the same as the previous phase. As the frequency changes, the phase of the impedance changes, so the phase relationship of the voltage and current will change.

You have an RL circuit, so the impedance is given by Z=R+iωL. At the new frequency ω', you should have Z'=R+iω'L. Note that the real part of the impedance doesn't change between the two cases; only the imaginary part does.

 

[viciado123]

Your mistake is in assuming the phase of the 6-amp current is the same as the previous phase. As the frequency changes, the phase of the impedance changes, so the phase relationship of the voltage and current will change.

You have an RL circuit, so the impedance is given by Z=R+iωL. At the new frequency ω', you should have Z'=R+iω'L. Note that the real part of the impedance doesn't change between the two cases; only the imaginary part does.

To find w' I need z'. How calculate z' ?

 

[vela]

Try solving for the magnitude of Z'. Since you know the real part, you can find the imaginary part and solve for ω.

 

[viciado123]

Try solving for the magnitude of Z'. Since you know the real part, you can find the imaginary part and solve for ω.

Xl = sqrt(25^2 - 9,97^2)
Xl = 22,93
w' = 1528,67 and f' = 243,3 (23,6% reduction)
Thanks

How I find maximum possible value for the current ?

 

[cartonn30gel]

How I find maximum possible value for the current ?

Think about how the magnitude of impedance changes in time. Does it stay constant? Does it have a minimum or a maximum? What should it be to yield the maximum value for the current?

 

[viciado123]

Think about how the magnitude of impedance changes in time. Does it stay constant? Does it have a minimum or a maximum? What should it be to yield the maximum value for the current?

The maximum value is when the imaginary part is 0.
Z = V / I = 150 / 9,97(real part) = 15A