Understanding Resistivity: Series or Parallel Circuit with an Inductor?

[pierce15]

Let's say I have some wire with known constant resistivity and I make a coil out of it. Can this schematically be considered a resistor in series or parallel with an inductor, or neither? The voltage drop across the resistor would have to always be the same as across the resistor, which suggests parallel... Any thoughts?

 

[Svein]

Can this schematically be considered a resistor in series or parallel with an inductor, or neither?

It is a series connection. Power resistors used to be produced that way.

Here are some power wirewound resistors:

 

[davenn]

Let's say I have some wire with known constant resistivity and I make a coil out of it. Can this schematically be considered a resistor in series or parallel with an inductor, or neither?

there is only 1 resistive component (only 1 component, period), there isn't anything in parallel with it, other than the power source ( which doesn't count in this case)

the wire in a coil is still going to be a resistor as shown in the pic's that Svein has shown ... particularly the top one.
BUT because it is a coil it is going to have significant inductanceDave

 

[sophiecentaur]

BUT because it is a coil it is going to have significant inductance

. . . . at a high enough operating frequency. No problem at 50HZ, though.
There is also a parasitic Capacitance (Parallel) that appears across the terminals. This will resonate with the nominal inductance and its effective inductance can be greater than nominal (approaching infinity at resonance). Thereafter, the component becomes capacitative. We're talking in terms of many tens of MHz or more (depending on the actual design of the Resistor. Resistors are often made with metal film with a spiral cut along the length of the cylinder (to trim the R value). That has a much lower inductance (only a very few turns) but the most expensive ones are trimmed during manufacture with a longitudinal groove (no spiral) and much better behaved at RF frequencies.
No component is ever exactly what's printed on the side!

 

[davenn]

There is also a parasitic Capacitance (Parallel) that appears across the terminals. This will resonate with the nominal inductance and its effective inductance can be greater than nominal (approaching infinity at resonance). Thereafter, the component becomes capacitative. We're talking in terms of many tens of MHz or more (depending on the actual design of the Resistor.

yup

Us ham radio guys would often used 50 Ohm wire wound resistors as higher power dummy loads and would have to use some parallel capacitance to negate the inductive effects so that the transmitter would see a load that looked "more' resistive than inductive.
This works great for the HF - VHF bands 1 - 150MHz. At 430 - 440MHz it became a little more touchy and we would often look for better
ways.Dave

 

[pierce15]

Alright... So if we put an AC voltage across the circuit, it can be analyzed using an impedance of $i\omega L + R$, where L is the well known inductance of a coil?

Also, how would you find what the theoretical capacitance of this setup would be?

 

[sophiecentaur]

Also, how would you find what the theoretical capacitance of this setup would be?

OMG! That would be pretty hard and would involve knowing the exact dimensions of the device, thickness of wire and pitch of helix, how it's actually mounted in the circuit (and operating frequency, of course). Best way to find it would be to by measuring the resonant frequency - a network analyser would give you a 'squeak' of the device in circuit and you would get a wiggle on the impedance response around the resonant frequency. In the old days, Marconi used to sell an instrument (can't remember the name but some PF member is sure to know) which could find the resonance and give you a direct reading of component values, as I recall. Very useful and practical for the RF Engineer before they invented the modern alternatives.