# Electrical Resistance (Easy Question)

## Homework Statement

A person gains weight by adding fat - and therefore adding girth - to his body and his limbs, with the amount of muscle remaining constant. How will this affect the electrical resistance of his limbs?
a. the resistance will stay the same
b. the resistance will increase
c. the resistance will decrease

## Homework Equations

$R=\frac{\rho L}{A}$

## The Attempt at a Solution

The answer is that the electrical resistance will decrease, but I don't get why. I get that the question hinted that area will increase ("adding girth"), which would make the resistance go down. But wouldn't resistivity also increase (fat has a higher $\rho$ than muscle)? This would make the resistance go up if it exceeded the effects of the increase in area.

Why is the answer that it will decrease resistance?

Thanks

BvU
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Difficult to give a hint and not spoil the exercise. Think about the amount of muscle tissue remaining the same.

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haruspex
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I think you are only supposed to consider resistance along the limb. Consider the fat and muscle as two separate resistors. What is their relationship in the limb, electrical circuit-wise?

• 1 person
I think you are only supposed to consider resistance along the limb. Consider the fat and muscle as two separate resistors. What is their relationship in the limb, electrical circuit-wise?

So if I'm not mistaken you can some them,

$\Sigma R = R_{muscle} + R_{fat}$

I think I can see why it would decrease now; just because more fat is being added doesn't make resistivity a bigger number. Fat was already present so the only number changing was A.

Thanks guys.

haruspex
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So if I'm not mistaken you can some them,

$\Sigma R = R_{muscle} + R_{fat}$
You are mistaken. That formula would mean the resistance increases.
You didn't answer my question: in terms of resistors in electrical circuits, what is the logical relationship between the fat along the limb and the muscle along the limb?

BvU
Homework Helper
I know this is physics, not democracy. But I'm inclined to agree with coop: more fat means less resistance from the fat, whether the resistances are in series or in parallel. There is simply more fat for the current to flow through.
Of course our entrails peeker is leading you towards one of the two and there I agree with him.

(Didn't the haruspices divine the future from this gory stuff ? Or do you mean that their future is our past?)

haruspex
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2020 Award
I know this is physics, not democracy. But I'm inclined to agree with coop: more fat means less resistance from the fat, whether the resistances are in series or in parallel. There is simply more fat for the current to flow through.
If you consider the muscle and fat as concentric cylinders, fat on the outer, and the electrical contacts are on the outer surface of the outer cylinder, you'll see it's not that simple. If the muscle is a very much better conductor then on a lean limb the current flows through a little fat, along the muscle, then through a little more fat. Increasing the fat layer adds resistance in series on that path.
(Didn't the haruspices divine the future from this gory stuff ? Or do you mean that their future is our past?)
You're right that the time order doesn't fit. Much of my life was spent studying the entrails of crashed computer software to determine what had happened.

BvU
Homework Helper
Poor coop.
Difficult to convince me. On our scale one conducting pad is under the left foot, the other under the right one. More fat means A increases, so R_fat decreases.
Your limbs and electrodes are a bit tougher, but L and A both increase linearly so I have at worst the same resistance ?
(The ? shows I'm not all that certain. Any biomedics around?)

haruspex
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Gold Member
2020 Award
Poor coop.
Difficult to convince me.
I'm not arguing that Coop's answer was wrong; in my first post on this thread I suggested we are supposed to consider only conduction along the limb, and that's still my position. But Coop's later post proffered the formula for resistance in series, which, if appropriate, should have led to the wrong conclusion.
Then you posted
more fat means less resistance from the fat, whether the resistances are in series or in parallel
which makes no sense to me. The only way I can understand that is if your model for the resistances being in series is a solid cylinder of fat joined end-to-end with a cylinder of muscle. My limbs do not follow that topology.

BvU