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Use kirchhoff's first law, so for two resistors in parallel: $$ I_\text{total}=I_1+I_2 $$ Then just use I=V/R $$ \\\frac{V}{R_\text{total}}=\frac{V}{R_1}+\frac{V}{R_2} $$ The voltage across any component, whether it be across resistor 1, 2, or the whole parallel portion of the circuit, is the same. It just cancels out so you can divide both sides by V.


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This is more intuitive if you think in terms of conductance, which is the inverse of resistance (1/R). When you put two equal resistors in parallel, you double the overall conductance. Why? You are adding a second path for current to flow, so you double that flow. Unfortunately, we tend to speak mostly in terms of resistance, which makes the math a bit ...


1

Two identical hoses with the same pressure difference between their ends will carry twice as much water as each does individually. So you get twice as much flow (current) for the same pressure difference (voltage), which is another intuitive way of thinking about Dave's Answer that it is more enlightening in this case to think in terms of conductances rather ...


1

A Zener is not like a normal diode. A normal diode lets current flow in only one direction and needs to be installed in the correct direction. A Zener diode is placed in the opposite direction, against the flow of current. A Zener diode will prevent current from flowing until it reaches a certain voltage, depending on the diode rating. Once this critical ...



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