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I was recently connecting a circuit together like here:

simple circuit

and I had the voltage set at 2V, with a 10Ω resistor. By Ohm's law, there was a current of 0.2A (and was confirmed by my multimeter). I accidentally touched both ends of the resistor...why wasn't I electrocuted? I thought the current necessary to kill a human was in the mA range.

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closed as off-topic by Norbert Schuch, ACuriousMind, Gert, Bill N, JamalS Feb 14 '16 at 17:49

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    $\begingroup$ Because your skin has a lot of resistance. $\endgroup$ – Mike Dunlavey Feb 13 '16 at 0:33
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    $\begingroup$ Because you have a much higher resistance than the resistor, so no current flowed through you. $\endgroup$ – Jon Custer Feb 13 '16 at 0:33
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    $\begingroup$ The current through the resistor is 0.2A but you're in parallel with the resistor, not in series. Parallel connected circuit elements have identical voltage across, not identical current through. $\endgroup$ – Alfred Centauri Feb 13 '16 at 0:34
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    $\begingroup$ Really the question is if you thought that accidentally touching exposed wires in your experiment would kill you, why did you proceed with the experiment? $\endgroup$ – user10851 Feb 13 '16 at 0:35
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    $\begingroup$ There are $2\,\text{Volts}$ across the resistor so according to $I = V/R$ there's $200\,\text{mA}$ going through it. Now you touch either side of the resistor. Your skin has, say, $10\,\text{k}\Omega$ resistance, so the $2\,\text{Volt}$ across your body produces $0.2\,\text{mA}$ current through you. There's no way $2\,\text{Volts}$ is ever going to kill you just from you touching it, because your skin has such a high resistance that such a low voltage puts a tiny current through you. The presence or absence of the resistor is completely irrelevant. $\endgroup$ – DanielSank Feb 13 '16 at 0:43
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Exactly you have a higher resistance than the other components thus as for same voltage current is inversely proportional to resistance, no current flows if resistance is very high and takes the path with low reistance and therefore even a voltmeter is made on the same principle.

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First off, what's dangerous about electricity isn't current — it's energy.

The power $P$ flowing through a circuit element with current $I$ undergoing voltage drop $V$ is given by $P=IV$. For your test circuit that is $\rm 0.2\,A \cdot 2\,V = 0.4\,W$, which is a quite modest power.

However, that's the power flowing through the resistor in the circuit that you drew. When you touched both leads of that resistor while the current was running, you added the impedance of your body in parallel with the resistance already in the circuit. A good ohmmeter will tell you that the resistance from one arm to the other is in the 100 k$\Omega$ range (but there's a lot of variation, mostly depending on whether your fingertips are sweaty or dry). A voltage drop of 2 V across a $10^5\,\Omega$ resistor gives a power of only $\rm 0.2\,nW$, entirely irrelevant to your body.

Note that for alternating currents, especially the 50-60 Hz currents used in electrical wall sockets around the world, interference between the frequency of the current and the oscillators that control your cardiac rhythm can screw up your heartbeat at a much more modest current. The (very) short story about electrical safety is not to worry about hurting yourself with 5-10 V power supplies, but don't mess around with the wall.

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