Click here to purchase the entire book in PDF format. Resistance and Ohm's Law Let's complicate matters a little by putting a constriction in the pipe - a small section where the diameter of the tube is narrower than anywhere else in the system. If we keep the same pressure difference created by the pump, then less water will go through because of the restriction - therefore, in order to get the same amount of water through the pipe as before, we'll have to increase the pressure difference. So the higher the pressure difference, the higher the flow; the greater the restriction, the smaller the flow. We'll also have a situation where the pressure at the input to the restriction is different than that at the output. This is because the water molecules are bunching up at the point where they are trying to get through the smaller pipe. In fact the pressure at the output of the pump will be the same as the input of the restriction while the pressure at the input of the pump will match the output of the restriction. We could also say that there is a drop in pressure across the smaller diameter pipe. We can have almost exactly the same scenario with electricity instead of water. The electrical equivalent to the restriction is called a resistor. It's a small component which resists the current, or flow of electrons. If we place a resistor in the wire, like the restriction in the pipe, we'll reduce the current as is shown in Figure 2.2. Figure 2.2: Equivalent situations showing the analogy between an electrical circuit with a battery and resistor to a plumbing network consisting of a pump and a constriction in the pipe. In both cases the flow (of electrical current or water, depending) runs clockwise around the loop. The higher the voltage difference, the higher the current. The bigger the resistor, the smaller the current. Just as in the case of the water, there is a drop in voltage (electrical ``pressure'') across the resistor. The voltage at the output of the resistor is lower than that at its input. Normally this is expressed as an equation called Ohm's Law which goes like this: Voltage = Current * Resistance or $$V = I R$$ (3.1) where V is in volts (abbreviated V), I is in amps (abbreviated A) and R is in ohms (abbreviated $\Omega$). We use this equation to define how much resistance we have. The rule is that 1 V of potential difference across a resistor will make 1 A of current flow through it if the resistor has a value of 1 $\Omega$. An ohm is simply a measurement of how much the flow of electrons is resisted. The equation is also used to calculate one component of an electrical circuit given the other two. For example, if you know the current through and the value of a resistor, the voltage drop across it can be calculated. Everything resists the flow of electrons to different degrees. Copper doesn't resist very much at all - in other words, it conducts electricity, so it is used as wiring; rubber, on the other hand, has a very high resistance, in fact it has an effectively infinite resistance so we call it an insulator