# Is a phase difference of 180 degree possible between emf and current?

While studying alternating currents I could read and observe through an oscilloscope that there can be phase difference between emf and current. But, is a phase difference of 180 degrees possible in a series LCR circuit?

No, a phase difference of 180º between applied voltage and current is not possible in a standard LCR circuit.

However, for reference, it is possible to construct electronic circuits that mimic negative resistance or negative impedance. In the case of negative resistance, $R = \dfrac{-V}{I}$. Here is a wikipedia article about it. This will, for a voltage sine wave produce a 180º phase shift in the current. These types of circuit can use inductors and capacitors and without going through all the possibilities there is probably a way of adding L, C and Rs around an op-amp to achieve it too.

Have a look at basic theory behind RLC circuits here.

Your circuit has a independent AC voltage source of angular frequency $\omega$ with RLC in series. The steady state solutions for $V$ and $I$ are sinusoidal in nature and these may be obtained by computing the impedance $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ of the circuit.

The phase difference between $V$ and $I$ is given as

$\tan\phi = (\frac{\omega L - \frac{1}{\omega C} }{Z})$

You can clearly see that $\phi \in (-\pi/2,\pi/2)$ from the above formula. So you cannot have a phase difference of $\pi$ between the two.

An intuitive explanation may be given as follows:

The average power generated by the AC source is given by $V_0I_0\cos(\phi)$ where $V_0$ is the amplitude of voltage, $I_0$ is the amplitude of current. If $\cos(\phi)$ is negative then you would get that the voltage source is generating average negative power and you would get a perpetual motion machine!

EDIT: I did not consider that case the OP might be asking the question in general, but I have answered the question for the specific case of ohmic resistance and all the parts of the circuit are passive components only.

But, is a phase difference of 180 degrees possible in a series LCR circuit?

Let's explore what it would mean if the phase difference were 180 degrees.

By the passive sign convention, positive current enters the positive terminal of a circuit element.

This means that when the instantaneous power is positive, energy flows to the circuit element and, when negative, energy flows from the circuit element.

So, if the voltage across and current through a circuit element were 180 degrees out of phase, the instantaneous power would always be negative, i.e., energy would always flow from the circuit element to the rest of the circuit.

Now, if the frequency of the source driving the series LCR circuit equals the LCR resonance frequency, the impedance seen by the source is purely real (resistive) and energy continuously flows from the source to the series LCR.

So, in this case and by the passive sign convention, the voltage and current associated with the source are 180 degrees out of phase, i.e., the source current exits the positive source terminal.

Now, the above will probably raise some eyebrows!