As we know that the current leads the voltage in capacitor and lags in inductor, what is the reason of the phenomenon?
As the capacitor opposes change in voltage and inductor opposes change in current, but how could leading, lagging phenomenon be explained by this?
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This is one of the characteristics of the sine wave. As the capacitor current is proportional to its terminal voltage derivative (i=c(dv/dt)) the sine wave of voltage produces a cosine wave current in it. A similar reason can be applied for the inductor.
This is one of the characteristics of the sine wave. As the capacitor current is proportional to its terminal voltage derivative (i=c(dv/dt)) the sine wave of voltage produces a cosine wave current in it. A similar reason can be applied for the inductor.
Information from this web page can help " http://hyperphysics.phy-astr.gsu.edu/hbase/electric/phase.html"
Physically the current in the capacitor is given by
i= C dv/dt
And the current in the inductor is given by
i= Integral v dt/L
This in case of the time domain behavior
In frequency domain one applies an alternating voltage on the device and observes the current. So,
Assuming v= Vm sinwt then
using the above equation one can get the response of the capacitor and inductor to harmonic signals in steady state:
Then i= wCVm cos wt = wCVm sin(wt +pi/4)
which means that the current leads the voltage by 90 degrees.
Also for the inductor
I = (Vm/ wL) sin (wt-90)
which means that the current lags 90 degrees behind the voltage in the inductor.
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FOR THE CAPACITOR WE HAVE
Q=CV
TAKING THE DERIVATIVE WE HAVE
dQ/dt=I=CdV/dt
TAKING THE LAPLACE TRANSFORM
I=CSV
PUTTING
S=jw
WE HAVE
I=jwCV
THIS MEANS CURRENT LEADS IN CAPACITOR
FOR INDUCTOR WE HAVE
FLUX=LI
TAKING THE DERIVATIVE WE HAVE
V=LdI/dt
TAKING THE LAPLACE TRANSFORM
V=LSI
PUTTING
S=jw
WE HAVE
V=jwLI
THIS MEANS THE CURRENT LAGS IN INDUCTOR
"As the capacitor opposes change in voltage..." that is capacitor needs some time to change the voltage across it ( explained by differential equation i(t)= C dv(t)/dt which means to change the voltage instantly either infinite current is required or infinitesimal capacitance is needed), but there is no such restriction to change current in capacitor. When the ac voltage(changing voltage) is given across the capacitor it needs time for that signal to pass through that capacitor. As I have already mentioned for current there is no restriction. That is why the voltage always lags the current in the case of the capacitor.
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