How do you solve this equation used to calibrate an ammeter?

[rexxii]

Homework Statement

algebra with two unknowns

Relevant Equations

two thetas in equation

Please can someone tell me how to solve the below:
we have been given:

can someone please explain how we deal with two theatas? please ignore full stops wouldn't line up any other way!​

 

[vela]

I can't tell what you're doing here or what the question is. Could you please fix your post and remove the formatting?

 

[rexxii]

I can't tell what you're doing here or what the question is. Could you please fix your post and remove the formatting?

Hi Vela, I apologise, new here. please see amendment

 

[Ray Vickson]

Please can someone tell me how to solve the below:
we have been given:

View attachment 241543

can someone please explain how we deal with two theatas? please ignore full stops wouldn't line up any other way!​

There is only one theta, not two. However, that theta appears in two places and in two different forms.

If you want to find the value of $\theta$ corresponding to a given current $i$, you can just draw a graph of $i$ vs. $\theta$ and pick out an approximate solution from the graph. You can refine it (i.e., get a more accurate solution) using any number of numerical equation-solving methods. Alternatively, you can submit the problem to a software package for solution. For example, using the EXCEL Solver tool should enable you to complete the job.

Another way is to re-write the equation as
$$\theta = (i/0.735)^2 \sin(\theta + 3),$$
plot the two curves $y = \theta$ and $y = (i/0.735)^2 \sin(\theta+30)$, and see where the two curves cross one another.

 

[rexxii]

There is only one theta, not two. However, that theta appears in two places and in two different forms.

If you want to find the value of $\theta$ corresponding to a given current $i$, you can just draw a graph of $i$ vs. $\theta$ and pick out an approximate solution from the graph. You can refine it (i.e., get a more accurate solution) using any number of numerical equation-solving methods. Alternatively, you can submit the problem to a software package for solution. For example, using the EXCEL Solver tool should enable you to complete the job.

Another way is to re-write the equation as
$$\theta = (i/0.735)^2 \sin(\theta + 3),$$
plot the two curves $y = \theta$ and $y = (i/0.735)^2 \sin(\theta+30)$, and see where the two curves cross one another.

hi,

thank you for the advice - i understand what you mean partly.

However, how can i define this on a graph? I cannot put theta into a graphing software.

I would have thought I plot y=3 and y=0.735 sqrt route (x/sin(x+30) but that doesn't seem to be working please could you expand on what you mean?

Thank you

 

[pasmith]

Graphing software generally expects the argument of sin to be in radians; your formula uses degrees.

However I think the intention is that you rearrange the equation as <br /> \theta = \left(\frac{3}{0.753}\right)^2 \sin(\theta + 30)<br /> as @Ray Vickson has done, and then iterate <br /> \theta_{n+1} = \left(\frac{3}{0.753}\right)^2 \sin(\theta_n + 30)<br /> to convergence, as can be done on a standard scientific calculator.

You will require an initial guess for \theta_0, and the first part of the question should provide that.

 

[Ray Vickson]

hi,

thank you for the advice - i understand what you mean partly.

However, how can i define this on a graph? I cannot put theta into a graphing software.

I would have thought I plot y=3 and y=0.735 sqrt route (x/sin(x+30) but that doesn't seem to be working please could you expand on what you mean?

Thank you

Show the details: why does it not work? It works for me, but I need to be careful about converting $\theta$ from degrees to radians.