# How can there be a path to ground with thick shoes and a carpet?

I'm connecting a test light to one pin of an halogen lamp. When I touch the metallic part on the back of the test light, the light glows, as it is supposed to. However, I have thick shoes and I am standing on a carpet. How could I possibly provide a path to ground?

I have tried:

• to stand on a plastic sheet -- the light still glows with the same intensity
• to touch a radiator with the other hand -- the light is much more intense
• to interpose my shoe between the metallic part of the test light and me -- the light does not glow
• to interpose a paper sheet -- the light still glows

Thank you for any response

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I'm not sure (hence a comment rather than an answer) but I think the path to ground is through the air. Your body provides a large surface area, making it easier for charge carriers (electrons? Ions? I don't know) to pass through the air to the conductive objects in the room. – Nathaniel Jan 22 '12 at 12:02
Perhaps you could test this hypothesis by attaching a large piece of tin foil to the contact instead of your body... – Nathaniel Jan 22 '12 at 12:03
My guess is that you form part of a capacitor that would saturate after a while. Have you tried long enough to see if the light diminishes after a while? – anna v Jan 22 '12 at 12:25
@Nathaniel I tried what you suggested and it worked, so thanks for your suggestion – Fiat Lux Jan 22 '12 at 12:52
@annav I think you would be right if my source were a DC supply, but it is alternated current, so I believe twistor59 is right – Fiat Lux Jan 22 '12 at 12:53

## 1 Answer

The pin you are touching has an alternating current power supply. One pin of the test light is connected to that A/C source. The other pin is connected to yourself. There will be a path to ground since you are capacitively coupled to the earth. An A/C current will flow through this capacitor. The size of your body helps in generating sufficient capacitance for this effect. You are a conductor (like one plate of a capacitor). The air, or shoe leather etc is the dielectric, and the earth is like the other plate of the capacitor.

In the other scenario, putting the shoe between your hand and the test light contact insulates you from the test light, but does not produce sufficient capacitance to conduct the A/C since the surface area of the test light (equivalent to one of the capacitor's plates) contact is far too small to produce a significant capacitance to yourself (equivalent to the other plate via the dielectric of the shoe.

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I think you are right, but could you explain how it is that the surface area of the test light is too small to produce a significant capacitance to myself, while there is a significant capacitance between myself and the Earth? I think I am very small compared to the Earth – Fiat Lux Jan 22 '12 at 12:58
The amount of current a capacitor will pass is proportional to the capacitance.  The capacitance depends on the geometry, in particular it goes up with increasing area of plates.  It's proportional to this area for a flat plate capacitor.  When you do the "hold the shoe" thing there are two capacitors in series : testlightpin-shoe-you, and you-air-ground. – twistor59 Jan 22 '12 at 14:57
If the effective area for you-air-ground is 1$m^2$ say, and the testlightpin-shoe-you is 1$mm^2$ say, then (ignoring the dielectric properties), the ratio of the capacitances is 1:1000000. Now the series capacitance is totally dominated by the smaller one (1/C = 1/C1+1/C2), which is the testlight-pin-you one by a factor of a million.  (Goodness knows how accurate the estimates are, but you get the general idea !) – twistor59 Jan 22 '12 at 15:02
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