LCR circuit and frequency equation

[Howlin]

Homework Statement

Im doing a lab experiment on LCR circuits and have gotten a graph of 1/capacatance against frequency^2. With my results I got the slope to be 0.89±0.01 and the intercept is 358708±43189

Homework Equations

the equation that was given was
frequency^2=(1/4*pi*L)[(1/C) - (R^2/2L)]
we then get
f^2 = 1/(4*pi*L*C) -R^2/(8*pi*L^2)

The Attempt at a Solution

since y =mx + c

the slope is
m=1/(4*pi*L) where m is 1/C
then c = -R^2/(8*pi*L^2)
we rearrrange the first equation to get L= 1/(4*pi*m) then when we know L we can get R
R^2 = -c*8*pi**l^2

When I put in my values for m for the first equation I get L = 2.85E-2 Henry
Then when to get R^2 I can as you can't the square of a negative number.

Would I get the positive of the R^2 value and then say the resistance is (plus/minus) 151 ohms?
Or can someone tell me what I am doing wrong
my lecturer does not know what is wrong so I kinda want to get it right

 

[anathema]

.

First, it's important to double check your calculations and make sure all of your units are consistent. For example, in your first equation, the units for m should be in units of 1/F (farads) and not Hz^2 (hertz squared). This may be causing some confusion in your calculations.

Next, it's important to consider the uncertainty in your slope and intercept values. The fact that your slope value has an uncertainty of 0.01 indicates that your data may not be very precise. This could be due to experimental error or limitations in your equipment. It's also possible that your data may not fit the theoretical equation very well, which could also contribute to the uncertainty.

In terms of finding the values for L and R, you can use your equations to calculate these values, but it's important to also consider the uncertainty in your calculations. For example, using your calculated value for m and its uncertainty, you can calculate a range of values for L, and similarly for R using your calculated value for c and its uncertainty. This will give you a range of possible values for L and R, rather than just a single value.

In terms of the sign of R, it's important to consider the physical meaning of the equation. In this case, R represents the resistance in the circuit, which cannot be negative. So when solving for R, you should take the positive value.

Overall, it's important to carefully consider your calculations and uncertainties, and to also take into account the physical meaning of the equations and your data. If you're still unsure, it may be helpful to consult with your instructor or a classmate for further clarification.