I know that in an purely inductive circuit the current lags behind voltage by $90^o$, in a purely capacitive circuit vice-versa and in an LCR circuit the current may lag or gain with respect to voltage depending on the value of capacitance and inductance. But, does this phase difference exist throughout the circuit?

To clarify what I'm asking consider the figure below. Assume the circuit is not in resonance and their is some phase difference. But, does the same phase difference exist between the current and voltage across the resistor? Can I find the same phase difference between them if I take any point in the circuit?

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1 Answer 1


Well the condition will be different for each component. Resonance doesn't matter. The current must obviously be identical in all three series elements. The Voltage across the resistance will be in phase with that current, and the Voltage across the capacitance must lag the current by 90 degrees, while the Voltage across the inductance must lead the current by 90 degrees. This makes the inductance and capacitance Voltages 180 degrees out of phase. At resonance they will be equal and opposite, so they cancel leaving just the whole source Voltage across the resistance.

  • $\begingroup$ Sir, then that means phase difference exists only within that particular component which causes it. Am I right? But, how does the current and voltage become in phase after passing through an inductor or capacitor? $\endgroup$ Commented Oct 26, 2013 at 5:35
  • $\begingroup$ Correct. Each element is pure L, R or C. The key is that the current is the same everywhere; (low frequency) So the Voltages are L di/dt, iR, & integral of idt, those three sum to the applied Voltage. The overall Voltage has some phase difference with the current, and that will depend on the resonance state. At frequencies below resonance the capacitive reactance will be higher, so the Voltage will lag the current by something less than 90 degrees, and above resonant frequency, the inductive reactance is larger so the Voltage will lead the current by something less than 90 degrees. $\endgroup$
    – user26165
    Commented Oct 26, 2013 at 6:28
  • $\begingroup$ I should point out that it is the VECTOR SUM of those three component Voltages, that equates to the input drive Voltage, so the L and C Voltages just subtract from each other, and then you have to do a little Pythagorean triangle calculation since the remaining vectors are 90 degrees apart, either leading or lagging the current. $\endgroup$
    – user26165
    Commented Oct 26, 2013 at 6:33
  • $\begingroup$ Sir, I'm still having some confusion. If the overall voltage has some phase difference with the current then, why there is no phase difference at any point on the circuit and only within the components which causes it? And when teachers say "the voltage lags behind the current or the current leads the voltage in a capacitor" it actually refers to the voltage lagging and the current is the same everywhere.Am I right? $\endgroup$ Commented Oct 26, 2013 at 6:37
  • $\begingroup$ Your circuit has a sinusoid Voltage source. The Voltage across the resistance is sinusoidal, and so is the current through it, and is given by Vr/R That current flows everywhere in the circuit, including inside the Voltage source. The Voltage across the inductance is sinusoidal, but at a phase angle 90 degrees ahead of the current. The Voltage across the capacitance is a sinusoid, but at a phase angle that lags the current by 90 degrees, so it is 180 degrees from the inductor Voltage. The vector sum of the Voltages equals the source V. The current phase varies with frequency. $\endgroup$
    – user26165
    Commented Oct 28, 2013 at 4:31

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