Does the impedance of RLC circuit change with time ?I think that it changes because in the beginning ,the opposition of the inductor is maximum then it begins to decrease as di\dt decreases and vice versa for the capacitor.one more reason , i also think since we represent impedance by a phasor then i think it should be changing with time , isnot it ?
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\$\begingroup\$ Think of the network RLC all together (steady state). Not the individual components. Impedance is generally a concept of steady state. \$\endgroup\$– MarlaCommented Dec 1, 2018 at 0:14
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\$\begingroup\$ Show some more maths for your theory so we can see your error. \$\endgroup\$– TransistorCommented Dec 1, 2018 at 0:16
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\$\begingroup\$ It's a function of frequency, not time. A phasor is a vector frozen in time, hence it's name change from vector to phasor. \$\endgroup\$– ChuCommented Dec 1, 2018 at 0:32
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\$\begingroup\$ I know that it depends on frequency ,but it was just an intuition \$\endgroup\$– Ahmed aliCommented Dec 3, 2018 at 23:26
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2 Answers
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The impedance of an idealized RLC circuit does not change with time. Your difficulty lies in the definition of "impedance", I think.
The impedance of a circuit at any given frequency describes how that circuit will operate in steady state. Strictly speaking, "steady state" means how the circuit responds to a sinusoidal (or constant) waveform that has been the same forever into the past, and will be the same forever into the future. Practically it just means how the circuit behaves after all the transients have settled out.
answered Dec 1, 2018 at 1:02
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\$\begingroup\$ Strictly, 'steady state' refers to the time domain. And there is no requirement for that state to extend past the here-and-now. \$\endgroup\$– ChuCommented Dec 1, 2018 at 9:04
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The simple answer is NO. The impedance of a RLC (either parallel or series or any configurations) doesn't change with time. It is only determined by the value of R, L, C, and the topology, and the frequency.
Before getting deeper, let's step back and think of a simpler case: the impedance of a resistor R = R1. What's its impedance? It is always R1. What if the we apply a sinusoidal voltage across it, it is still R1. The point is the impedance of R is determined by its material and geometrical property. It doesn't change with time, or voltage across it.
Now, how about a capacitor C = C1? Its impedance is then Zc= 1/(2*pifC1). Now there are two parameters in the formula: the capacitance C1, which again is determined by material and geometrical properties of the capacitor, and frequency f.
Similar argument applies to inductors. For an indutor of value L1. Zl = 2pifL1.
Then consider a series RCL network. Z_rcl = R + 1/(2*pifC) + 2*pifL.
Please note this is expression in Fourier domain. But regardless in which domain I write the formula, the physical significance won't change.
However, the concept of reactive components (C and L) impedance are developed in the context of frequency domain analysis. To discuss their impedance outside of this context is somehow meaningless.
Your feeling of "the opposition of the inductor is maximum then it begins to decrease" is not a change of impedance, but simply the fix impedance doing it job where an AC signal applies to the network. (Also, try to describe the process mathematically. You may have a better understanding.)
On the other hand, in real world, since the material makes of R C L does age through time and their property varies across temperature, moisture, voltage across them, frequency due to sink effect and so on, a real RCL network's impedance does vary over the time. But this is because the value of R C L changed, not the process you described.
Hope that helps.
