Calculate Frequency of RLC Series Circuit with R=1kOhms, L=100mH, C=1uF

[jayhar]

Given that R = 1 kOhms, L=100mH and C = 1uF, calculate the frequency at which the current in the circuit lags the supply voltage by 45deg.

Show how the impedance of the circuit is given by Z = sqr root R2 + (wL - 1/wC)2
arctan [(wL - 1/wC) / R]

I have not been given any information regarding supply voltages or frequencies.
I can not see how i can calculate impedance with no frequencies.

I am assuming for Q1 that tan theta = XL-XC/R, this can only be 1000/1000 = 1 = 45deg.

 

[CEL]

You already have that $$X_L - X_C = 1000$$
Write the impedances as functions of L and C (known) and the frequency (unknown).
You have one equation with one unknown, so you can calculate it.
Use the calculated frequency to obtain the impedance.

 

[piercas]

Thank you for providing the information for the circuit components, R, L, and C. To calculate the frequency at which the current lags the supply voltage by 45 degrees, we can use the formula f = 1 / (2π√(LC)), where f is frequency, L is inductance, and C is capacitance. Plugging in the values, we get f = 1 / (2π√(100mH * 1uF)) = 159.155 Hz. This is the frequency at which the current will lag the supply voltage by 45 degrees in an RLC series circuit with the given components.

To calculate the impedance of the circuit, we can use the formula Z = √(R^2 + (ωL - 1/ωC)^2), where ω is the angular frequency, given by ω = 2πf. Plugging in the values, we get Z = √(1000^2 + ((2π*159.155)*(0.1) - 1/(2π*159.155)*(10^-6))^2) = 1000 Ω. This is the total impedance of the circuit, which includes the resistance, inductance, and capacitance components.

We can also use the formula Z = R + j(XL - XC), where j is the imaginary unit. Plugging in the values, we get Z = 1000 + j((2π*159.155)*(0.1) - 1/(2π*159.155)*(10^-6)) = 1000 + j(100 - 100) = 1000 Ω. This also gives us the same result for the impedance of the circuit.

To find the phase angle, we can use the formula θ = arctan((XL - XC)/R). Plugging in the values, we get θ = arctan((2π*159.155)*(0.1) - 1/(2π*159.155)*(10^-6)/1000) = arctan(100/1000) = arctan(0.1) = 5.71 degrees. This is the angle by which the current lags the supply voltage in the circuit.

Overall, we can see that the impedance of the circuit is determined by the values of R, L, and C, and the frequency