The difference between impedance and resistance


My Dad would be ashamed for me for writing this thread (he had a background in electrical engineering) but can someone explain the differnce between impedance and resistance (other than the former is for ac and the latter dc) as it pertains to audio circuitry?
russellrcncom
"Impedance" is a broader term than "resistance," and reflects the opposition to current flow that can be imposed by resistance, capacitance, or inductance.

The impedance of an ideal resistor (in practice there is no such thing, as all resistors will also have some amount of inductance and capacitance) is the same as its resistance and is the same at all frequencies. Resistance is usually denoted as R and is measured in ohms.

The impedance of an ideal capacitor (again, there is no such thing) decreases as frequency increases, and is equal to:

Xc = 1/(2 x pi x f x C)

where Xc denotes what is referred to as capacitive reactance (one form of impedance), and is also measured in ohms;
f = frequency in Hertz
C = capacitance in Farads

The impedance of an ideal inductor (again, there is no such thing) increases as frequency increases, and is equal to:

Xl (that's a small "L", not the number "1" or a capital "i") = 2 x pi x f x L

where Xl denotes what is referred to as inductive reactance (one form of impedance), and is also measured in ohms;
f = frequency in Hertz
L = inductance in Henries

Depending on the frequency and the circuit application, it is often (but certainly not always) possible to treat a practical resistor as being a close enough approximation to an ideal resistor to neglect its stray capacitance and inductance, as well as other non-ideal effects it may have. Likewise for practical capacitors and inductors.

The combined impedance of some amount of inductance, capacitance, and resistance is NOT calculated by directly combining the number of ohms of each, because the three parameters have different effects on the phase relation between voltage and current.

In the case of a pure resistance, voltage and current are in phase with each other. In the case of a pure inductance, voltage leads current by 90 degrees (1/4 cycle of the signal frequency). In the case of a pure capacitance, voltage lags current by 90 degrees.

Given that, the magnitude of the impedance of a circuit element combining all three types of impedance is calculated, for a specific frequency, by subtracting Xc from Xl, and then taking the square root of the sum of the squares of that difference and R. The phase angle between voltage and current at a specific frequency, corresponding to that combined impedance, is equal to the (arctangent of ((Xl-Xc)/R)), among other ways that it can be calculated.

Best regards,
-- Al
Holy shit.
Great answer.
I always wondered about this.
Thank you very much, Al!
Sincerely,
Truman
Al, Could you please add your take on Power Factor?
The Wiki article says that when the phase angle is 90degrees NO power is delivered.
My 'pet' idea is that reactive speaker loads are what really defines a 'bad load', not merely low impedance.
Hi Magfan,

Yes, your statements are correct, and the posts you have made emphasizing the importance of phase angle and how resistive vs. reactive a speaker load is are good.

A pure inductance or capacitance (with a phase angle of plus or minus 90 degrees) cannot dissipate (consume) any power at all.

Consider a sine wave at some frequency, with a phase angle of 90 degrees between voltage and current. When the sine wave reaches its maximum voltage, current will be zero. When current reaches its maximum, voltage will be zero. Since the power dissipated (consumed) at any instant of time is the product (multiplication) of voltage and current at that time, power at those instants will be zero.

In between those times, the product of voltage and current will alternate each quarter-cycle between being positive and being negative. That can be seen by drawing out two sine waves, with one delayed by 90 degrees from the other.

The alternating polarities correspond to the fact that incoming energy is stored during one quarter-cycle, and then discharged back to the source during the next. So the net power dissipation in the load is zero, and the energy that the amplifier tries to send to the speaker winds up being dissipated in the amplifier as heat.

In a purely resistive load, all incoming energy is consumed by the load. Voltage and current are always in phase, and their product is always positive. During positive-going quarter cycles the power is the product of two positive numbers, which is positive, and during negative-going quarter-cycles it is the product of two negative numbers, which is also positive.

Power factor, as defined here, reflects the degree to which the load is resistive vs. reactive, with a value of 1 being purely resistive, and 0 being purely reactive (capacitive or inductive). A value of 1 will correspond to a phase angle of 0 degrees, and a value of 0 will correspond to a phase angle of plus or minus 90 degrees.

Best regards,
Al
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