# Why Does a Resistor Show Different Values in AC and DC Measurements?

• The_Lobster
In summary: These effects can be modeled (and measured) and therefore correct values of the resistance can be obtained. However, in high frequency circuits (e.g. radio transmitters), these effects can be significant and lead to major errors in resistance measurement.In summary, the resistance of a resistor may have a different value when measured with a sine wave signal (AC) than when measured with a direct current (DC) source due to factors such as skin effect, inductance, and capacitance. To obtain accurate resistance measurements in AC circuits, the rms values of the voltage and current must be used. In high frequency circuits, these effects can lead to significant errors in resistance measurement.
The_Lobster

## Homework Statement

If possible, find reasons why the resistance of a resistor may have a different value when measured with a sine wave signal (a.c.) than when measured with a d.c. (dirrect current) source.

## The Attempt at a Solution

Please correct me if anything of what I've said below could be wrong in some way:

In an AC circuit, the sinusoidal current through a resistor is given by: $$i = Isin \omega t$$. From Ohm's law, the instantaneous potential $$v_R$$ is: $$v_R = iR = (IR)sin \omega t = V_R sin \omega t$$.

What I don't get here, is that, according to the equation $$v_R = iR$$, the relationship between the instantaneous voltage and current is constant (giving R), but if we graph this, since the two are in phase, both the current and the voltage across the resistor will be 0 once every cycle. Doesn't that mean that the resistance, R, of the resistor will also vary? In this illustration: http://www.electronics-tutorials.ws/resistor/res32.gif , we also see that the voltage has steeper curves than the current, and they're not proportional, so $$v_R = iR$$ isn't true? I find this really confusing...

If we only look at the peak voltages, the resistance would be the peak of the voltage divided by the peak of the current.. it's only when we're talking about instantaneous current and voltage I'm getting confused...

Aside from what I've written above, whenever the frequency of the changing current in a circuit is any other than 0 (DC), any circuit element will exhibit some combination of resistive, capacitive and inductive behaviour. May this mean that we might see a slight drop in resistance measured on the resistor because of the "imagined" inductor in series with it?

Lastly, I read about something called the "skin effect" and the proximity effect that might effect circuit elements when there's an alternating current. Is this something different than the above? Or is it simply another way of saying that each element exhibits some inductive, capaticive, etc. behaviour?

J:-)

The_Lobster said:

## Homework Statement

If possible, find reasons why the resistance of a resistor may have a different value when measured with a sine wave signal (a.c.) than when measured with a d.c. (dirrect current) source.

## The Attempt at a Solution

Please correct me if anything of what I've said below could be wrong in some way:

In an AC circuit, the sinusoidal current through a resistor is given by: $$i = Isin \omega t$$. From Ohm's law, the instantaneous potential $$v_R$$ is: $$v_R = iR = (IR)sin \omega t = V_R sin \omega t$$.

What I don't get here, is that, according to the equation $$v_R = iR$$, the relationship between the instantaneous voltage and current is constant (giving R), but if we graph this, since the two are in phase, both the current and the voltage across the resistor will be 0 once every cycle. Doesn't that mean that the resistance, R, of the resistor will also vary? In this illustration: http://www.electronics-tutorials.ws/resistor/res32.gif , we also see that the voltage has steeper curves than the current, and they're not proportional, so $$v_R = iR$$ isn't true? I find this really confusing...

If we only look at the peak voltages, the resistance would be the peak of the voltage divided by the peak of the current.. it's only when we're talking about instantaneous current and voltage I'm getting confused...

Aside from what I've written above, whenever the frequency of the changing current in a circuit is any other than 0 (DC), any circuit element will exhibit some combination of resistive, capacitive and inductive behaviour. May this mean that we might see a slight drop in resistance measured on the resistor because of the "imagined" inductor in series with it?

Lastly, I read about something called the "skin effect" and the proximity effect that might effect circuit elements when there's an alternating current. Is this something different than the above? Or is it simply another way of saying that each element exhibits some inductive, capaticive, etc. behaviour?

J:-)

When measuring AC quantities you use rms. So the resistance is the ratio of the rms of the voltage and the rms value of the current.
The reasons to measure different values in AC and DC are the other ones you cited: skin effect (most resistors are made of a thin layer of conductive material over a ceramic substrate), inductance and capacitance.

## 1. What is the difference between a resistor value in AC vs DC?

The main difference between a resistor value in AC (alternating current) and DC (direct current) is the way in which the current flows. In AC, the current changes direction periodically, while in DC, the current flows in only one direction. This leads to differences in the behavior of resistors in these two types of circuits.

## 2. Are resistor values different for AC and DC circuits?

Yes, resistor values can be different for AC and DC circuits. This is because the behavior of resistors is influenced by the frequency of the current, which is different in AC and DC circuits. In AC circuits, the resistor values are affected by both the amplitude and frequency of the current, while in DC circuits, the resistor values are only affected by the amplitude of the current.

## 3. How do I calculate the value of a resistor in an AC circuit?

The value of a resistor in an AC circuit can be calculated using Ohm's law, which states that the voltage (V) across a resistor is equal to the current (I) multiplied by the resistance (R). However, in AC circuits, the voltage and current are constantly changing, so the calculation must take into account the peak or RMS (root mean square) values of both the voltage and current.

## 4. Can I use the same resistor for both AC and DC circuits?

In some cases, you can use the same resistor for both AC and DC circuits. This is especially true for low frequency AC circuits, where the resistor values needed are similar to those for DC circuits. However, for high frequency AC circuits, special types of resistors, such as high-frequency or non-inductive resistors, may be needed to ensure accurate and stable performance.

## 5. How does the type of resistor affect its value in AC vs DC circuits?

The type of resistor can affect its value in AC vs DC circuits in several ways. Firstly, the material of the resistor can influence its resistance and temperature coefficient, which can affect its value in both types of circuits. Additionally, the physical construction of the resistor, such as its size, shape, and leads, can also impact its value in AC and DC circuits differently. Therefore, it is important to carefully select the appropriate type of resistor for the specific circuit and application.

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