# Resistor's behaviour at high frequencies Looking at the impedance vs. frequency graph

1) At low-frequencies Z=R and hence it would be a straight line.

2) For mid-frequencies, Z decreases possibly due to capacitance, but I'm not sure exactly why.

3) The inductor characteristic jwl would dominate and hence it would continue to exponentially increase.

What I am confused about is the midsection here. Why does Z dip down to form a minimum and then rise?

• As Frequency Increases the Reactive Capacitance bypasses the resistance and forms a resonant LC circuit. It's curve like that because the increasing frequency decreases reactive capacitance while also increasing the resonant frequency and the reactive inductance. The Q-factor of the RLC circuit increases when the slope of the line on either side of the resonant frequency gets steeper. if F=1000 and C=.1uF then Xc=1/(2*pi*1000*.0000001)=1591-Ohms, F=10k Xc=159, if L=.253 then at f=1000 the Xl=2*pi*1000*.5=1,591-ohms and at f=10k Xl=15,910-Ohms. – Danny Sebahar Dec 8 '18 at 16:31

Capacitance exists between any two points of differing potential.

The resistor has (quite reasonably) metal pads or leads (depending on type) for mounting and therefore you have two conductors at some space apart at different voltages (it is a resistor after all) which forms a capacitor in parallel with the resistor. There is also series inductance, so we get the below item: simulate this circuit – Schematic created using CircuitLab

Equivalent circuit of a resistor for ac analysis

You will notice that we have a damped series LC resonant circuit. In series resonance, the impedance goes to a minimum at resonance (the dip in the graph).

The circuit is capacitive below resonance and inductive above it, so that is why you see the dip (resonance) and then the increase (inductive reactance eventually exceeds the value of the resistor).

• why is the capacitor in series with the resistor – fred Dec 8 '18 at 18:47
• why would the capacitor dominate at medium range frequencies? – fred Dec 8 '18 at 20:34