It seems to me that since you haven't studied the use of the complex operator j, it's going to be difficult for you to solve this problem.

The name "reactance" only applies to a pure inductor or capacitor. If there is a resistance associated with the inductor (winding resistance), the name given to the combination is "impedance".

So, where you have the expression 'Xl=wrL", you are trying to show the total opposition to current and this expression is wrong. It should be Z = SQRT( r^2 +(wL)^2), where Z is the impedance, not reactance. The same applies to your expression Xc=1/wrC; it should be Z = SQRT( r^2 +(1/wC)^2), but in your problem circuit, there isn't a resistance associated with the capacitor.

You also have the formula for Fr wrong; it should be:

Fr = 1/2pi SQRT(1/LC - (R/L)^2)

Finally, the total current does not split equally in the two branches. The inductor current is composed of two parts, a real part and an imaginary part (there's where the j operator comes in). The capacitor current is a pure imaginary current, equal in value to the imaginary part of the inductor current, and it "cancels" out the imaginary part of the inductor current, leaving only a pure real current for the total current. That's why the total current is in phase with the applied voltage.

I don't see how you can solve this problem without the use of the j operator, unless you are given a formula for the total impedance of the parallel circuit in terms of r, L, C and w. I showed how to derive such a formula in post #15, but you need to use j to finish the derivation.

Maybe you should ask your tutor if there is some formula he expects you to find, and where you might find it, because I don't see how you can derive it yourself without using j.

I'll give you a hint to help you determine if you're making any progress: the inductor value is .0504073 H.

 

It seems to me that since you haven't studied the use of the complex operator j, it's going to be difficult for you to solve this problem.

The name "reactance" only applies to a pure inductor or capacitor. If there is a resistance associated with the inductor (winding resistance), the name given to the combination is "impedance".

So, where you have the expression 'Xl=wrL", you are trying to show the total opposition to current and this expression is wrong. It should be Z = SQRT( r^2 +(wL)^2), where Z is the impedance, not reactance. The same applies to your expression Xc=1/wrC; it should be Z = SQRT( r^2 +(1/wC)^2), but in your problem circuit, there isn't a resistance associated with the capacitor.

You also have the formula for Fr wrong; it should be:

Fr = 1/2pi SQRT(1/LC - (R/L)^2)

Finally, the total current does not split equally in the two branches. The inductor current is composed of two parts, a real part and an imaginary part (there's where the j operator comes in). The capacitor current is a pure imaginary current, equal in value to the imaginary part of the inductor current, and it "cancels" out the imaginary part of the inductor current, leaving only a pure real current for the total current. That's why the total current is in phase with the applied voltage.

I don't see how you can solve this problem without the use of the j operator, unless you are given a formula for the total impedance of the parallel circuit in terms of r, L, C and w. I showed how to derive such a formula in post #15, but you need to use j to finish the derivation.

Maybe you should ask your tutor if there is some formula he expects you to find, and where you might find it, because I don't see how you can derive it yourself without using j.

I'll give you a hint to help you determine if you're making any progress: the inductor value is .0504073 H.

Actually it can be explained with the Pythagorean Theorem. for the trig-aversed crowd. (The squaw on the hippopotamus is worth the sum of the squaws on the other two hides).

Eric

 

Sorry i havent replied in a while but having contacted my tutor and im given this formula :


ωparallel√ωseries-(1/CRd)sq

this is derived for a host of formulas,and C is now the only unknown.

Thanks for all your help guys,and showing different ways to approach this problem.

Merry christamas all !
Cheers
Rubberfrog

 

So what do you get for R, L and C?