What Is the Frequency of the Voltage Source in an LRC Series AC Circuit?

[Fisicks]

Homework Statement

An ac voltage source is connected in series with a 1 uF capacitor and a 750 ohm resistor. The amplitude of the voltage source is measured to be 4V rms while the voltages across the resistor and across the capacitor are 3V rms and 2.7V rms respectively. Determine the frequency of the voltage source.

Homework Equations

The Attempt at a Solution

I said that the current going through the resistor is 250, and then Z=(750^2 + (1/wC)^2)^1/2. So i let 4/250=Z but this isn't right, where am i going wrong?

Thanks guys

 

[cepheid]

This is just an RC circuit (no inductor). Anyway, one the problems I can see with your calculations is that if

V_R = IZ_R = IR,

Then I = V_R/R = 3 V_rms / 750 ohm = 4 mA_rms

not 250 A.

 

[Fisicks]

Ok, so I would do 4/(4x10^-3)=Z then?

 

[cepheid]

Ok, so I would do 4/(4x10^-3)=Z then?

It should work. Did you try it? Based on your first post, it seems like you know what the correct answer is supposed to be.

 

[rwisz]

!

I would first clarify the units being used for the resistor and capacitor. Are they in ohms and farads respectively? This is important for accurately calculating the impedance.

Assuming they are in the correct units, I would approach this problem by first finding the total impedance (Z) of the circuit using the formula Z = √(R^2 + (1/ωC)^2), where R is the resistance and ω is the angular frequency. From the given information, we can plug in the values to get Z = √(750^2 + (1/ω(1x10^-6))^2) = 750.31 ohms.

Next, we know that the rms voltage across the resistor (VR) is 3V and the rms voltage across the capacitor (VC) is 2.7V. Using Ohm's law (V = IR), we can find the rms current (I) in the circuit. For the resistor, I = VR/R = 3/750 = 0.004A. For the capacitor, I = VC/Z = 2.7/750.31 = 0.0036A.

Now, we can use the fact that the total current in a series circuit is equal to the sum of the individual currents. Therefore, I = 0.004 + 0.0036 = 0.0076A. Since we know that I = V/Z, we can rearrange this equation to solve for ω, which gives us ω = V/IZ = 4/(0.0076x750.31) = 697.37 rad/s.

Finally, we can convert this angular frequency to frequency (f) by dividing by 2π, giving us a frequency of approximately 111 Hz.

In conclusion, the frequency of the voltage source in this LRC series AC circuit is approximately 111 Hz.