All the complex power supplied to the circuit must be absorbed by the two inductors in the circuit.Can anyone explain how i can go about solving this problem?
well using the nodal analysis if i find the current through inductor, what then? how to obtain value of L.
thanks
It's hard to say since there are two sources in the circuit. But it's definitely one of those sanity checks that should be performed. It may be correct, but sufficient analysis should be done to establish that it really is correct and it really does make sense that it works out the way that it does.It would be surprising that the source produces leading power factor. It might be worth checking the complex phasor angle is negative rather than positive.
Demons lie along that path.All the complex power supplied to the circuit must be absorbed by the two inductors in the circuit.
Figure out how much complex power the known inductor is absorbing and what remains must be absorbed by the unknown inductor L.
From here you should be able to deduce the value of L.
If you want to know the value of a resistor, you need to know BOTH the voltage across it and the current through it at the same moment in time. The same is true for a capacitor or an inductor. In the time domain, you need the value of one and the derivative of the other at the same moment in time. In the phasor domain, the complex impedance takes care of this for you and, like the resistor, you just need to know BOTH the phasor voltage across it and the phasor current through it, combined with the impedance for an inductor.Can anyone explain how i can go about solving this problem?
well using the nodal analysis if i find the current through inductor, what then? how to obtain value of L.
thanks
You are absolutely right. Goes to show one shouldn't assume anything without some careful thinking. It's actually a great problem.It's hard to say since there are two sources in the circuit. But it's definitely one of those sanity checks that should be performed. It may be correct, but sufficient analysis should be done to establish that it really is correct and it really does make sense that it works out the way that it does.
If a cap is used instead of an inductor the effective impedance would have the formTaking your answer, it would appear that if the "inductor" were actually a 2.16mF capacitor, it would come close to satisfying your solution.
Agreed. I said a cap would be close, not exact. Using a 2.16F cap would yield a branch impedance (including the 20Ω resistor) of (17.67-j5.293)Ω. I suppose an arguably closer match could be had with a slightly larger cap to spread the error between the two.So it's clear even this approach wouldn't give a solution either. I can't equate the 3 elements comprising the required Zp [L replaced by C] with the given value constraints - notwithstanding the open choice of capacitance.
If I removed the 3 existing elements in parallel with the current source & placed a series impedance Zs=16.475-j5.293 Ω in parallel with the current source then the result would be consistent.
Sir, in the step where you calculate current from the voltage source then finding the voltage drop across the impedance \[(14 + j7)\]Ω, don't we have to take in account the current from the current source?Per the recommended caution regarding my assumption I've attempted to solve the problem.
My approach was
Problem is I end up with Zp=16.475-j5.293 Ω which is incompatible with the unknown branch equivalent of [20Ω||(12+jXL)]. So I'm stumped if there is a solution.
- Choose a suitable reference point on the circuit.
- Assume the complex power from the voltage source is correct - I assume the source delivers a leading power factor.
- Calculate the current from the voltage source.
- Calculate the drop in the series 14Ω + 7/8H section [I'll call it Vd]
- Calculate the resulting voltage across the current source [I'll call it Vp]
- Find the total current Ip into the parallel branch [20Ω||(12+jXL)] - Current from step 2 above + 2A
- Calculate the branch impedance Zp=Vp/Ip
- Equate the value Zp to the parallel section comprising [20Ω||(12+jXL)] to determine XL and hence L.
How would you take it into account?Sir, in the step where you calculate current from the voltage source then finding the voltage drop across the impedance \[(14 + j7)\]Ω, don't we have to take in account the current from the current source?
I think you've missed the point.So it means that the current we arrive at using the complex power delivered by Voltage source in this circuit is actually the sum of currents from the current source and the current due to the voltage source, i.e it implies? am i right sir.
So the same voltage source for the same impedance configuration would deliver a different complex power in the absence of the current source?
Yes, on all points. The voltage source does not live in isolation. It is part of a circuit and the power it provides (or absorbs) is a result of the total interaction of that source with the entire circuit. Change the circuit and you change the interaction.So it means that the current we arrive at using the complex power delivered by Voltage source in this circuit is actually the sum of currents from the current source and the current due to the voltage source, i.e it implies? am i right sir.
So the same voltage source for the same impedance configuration would deliver a different complex power in the absence of the current source?
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