Zero in a basic RC high pass filter

If I write the transfer function I can clearly see a zero at zero frequency and a pole at 1/2πRC frequency. But If I simply look at this circuit I would say that there is one pole and no zero(as there is only one path from input to output(that's one technique I learnt in my engineering)). Is there any intuitive explanation of this zero or am I making some mistake? Please explain.

2 Answers

For a low-pass or a high-pass simple RC filter, there is always a pole and always a zero. For the low-pass the zero is at infinity i.e. infinite frequency. For high pass, it is at zero frequency (aka DC).

But If I simply look at this circuit I would say that there is one pole and no zero

If I look at it I see a DC blocking capacitor hence the output cannot have DC content hence there is a zero at DC (0 hertz).

Having any energy storing element (inductor or capacitor) implies there is a pole. In-fact, the number of poles is always equal to the number of independent energy storage elements present in the circuit. Thus, this circuit has one pole.
For checking the number of zeros, you need to short circuit a capacitor (or open circuit an inductor) and see if the resulting circuit still has non-zero transfer function. The number of independent energy storage elements you can short simultaneously determines the number of zeros.
In your case, if you short the capacitor, your transfer function is unity (non-zero), hence there is one zero in the circuit.