Then Ohm's law says that V must equal I times R. Where R represents the resistance that the material offers to the flow of charges through that material.
And we have talked in detail about this in a previous video, so if you need a refresher it will a great idea to go back and watch that video and then come back over here. And so the question is, if I have some material with me, how do I check, practically, whether this relationship, Ohm's law, whether it really holds true or not.
So to do this, we need to first understand a little bit more about this thing called resistance. You see, the resistance is a property of the material and its dimensions and something we'll talk more about in the future.
What's important is that it does not depend on the values of voltage or current. So even if we change these values, for any given material, like let's say we have for a given wire, let's say, as we change the values of the voltage or the current, this number shouldn't change. In other words, in this equation, this number is a constant. This is a constant. And so, another way to look at this, is we could say if we divide this equation by I, we could say V divided by I should equal R, should be a constant.
Should be a constant. So to check whether any material obeys Ohm's law, we need to check whether the ratio of voltage and current through that material, is it a constant? It means if we double the voltage, the current must also get doubled because the ratios should remain the same. If we triple the voltage, the current must also get tripled. That's the basic idea behind Ohm's law. So how do we practically test this? Well one easy way to do this is by drawing a graph.
So what we like to do is we like to plot the values of voltage along the Y axis and the values of current along the horizontal X axis. So let's say we put some value of voltage. Let's say we put a value of 2 volts, as an example, and we measure the current and let's imagine the current turns out to be ine ampere. Then we'll plot that point over here in our graph. Now, if Ohm's law is valid, then when I double the voltage, if I double the voltage, let's say I make it 4 volts, then the current must get doubled.
All right? The current must get doubled, so two amperes. So the next point, our other point, must lie somewhere here. And similarly, if I triple the voltage, so let's say I triple it, triple the voltage, so I make it sux volts, then the current must also get tripled, three amps, and so that point would lie somewhere over here.
Conductance and resistance are reciprocals. The resistance of an object depends on its shape and the material of which it is composed. The cylindrical resistor is easy to analyze, and by so doing we can gain insight into the resistance of more complicated shapes.
The longer the cylinder, the more collisions charges will make with its atoms. The greater the diameter of the cylinder, the more current it can carry again, similar to the flow of fluid through a pipe. Cylindrical Resistor : A uniform cylinder of length L and cross-sectional area A. Its resistance to the flow of current is similar to the resistance posed by a pipe to fluid flow. The longer the cylinder, the greater its resistance.
The larger its cross-sectional area A, the smaller its resistance. As mentioned, for a given shape, the resistance depends on the material of which the object is composed. Different materials offer different resistance to the flow of charge.
In contrast, the resistance R is an extrinsic property that does depend on the size an shape of the resistor. Recall that an object whose resistance is proportional to the voltage and current is known as a resistor. What determines resistivity? The resistivity of different materials varies by an enormous amount. For example, the conductivity of teflon is about times lower than the conductivity of copper.
Why is there such a difference? Likewise, resistors range over many orders of magnitude. The potential difference voltage seen across the network is the sum of those voltages, thus the total resistance the series equivalent resistance can be found as the sum of those resistances:. As a special case, the resistance of N resistors connected in series, each of the same resistance R, is given by NR. Resistors in a parallel configuration are each subject to the same potential difference voltage , however the currents through them add.
Thus the equivalent resistance Req of the network can be computed:. For the case of two resistors in parallel, this can be calculated using:. A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other, such as is shown in. Resistor Network : In this combination circuit, the circuit can be broken up into a series component and a parallel component.
However, some complex networks of resistors cannot be resolved in this manner. These require a more sophisticated circuit analysis. One practical application of these relationships is that a non-standard value of resistance can generally be synthesized by connecting a number of standard values in series or parallel.
This can also be used to obtain a resistance with a higher power rating than that of the individual resistors used. In the special case of N identical resistors all connected in series or all connected in parallel, the power rating of the individual resistors is thereby multiplied by N. Resistance, Resistors, and Resistivity : A brief overview of resistance, resistors, and resistivity.
Resistivity and resistance depend on temperature with the dependence being linear for small temperature changes and nonlinear for large. Compare temperature dependence of resistivity and resistance for large and small temperature changes. The resistivity of all materials depends on temperature. Some materials can become superconductors zero resistivity at very low temperatures see.
Conversely, the resistivity of conductors increases with increasing temperature. Since the atoms vibrate more rapidly and over larger distances at higher temperatures, the electrons moving through a metal, for example, create more collisions, effectively making the resistivity higher. Resistance of a sample of mercury : The resistance of a sample of mercury is zero at very low temperatures—it is a superconductor up to about 4.
Above that critical temperature, its resistance makes a sudden jump and then increases nearly linearly with temperature. Some alloys have been developed specifically to have a small temperature dependence. This is useful for making a temperature-independent resistance standard, for example.
They become better conductors at higher temperature because increased thermal agitation increases the number of free charges available to carry current. Numerous thermometers are based on the effect of temperature on resistance see. One of the most common is the thermistor, a semiconductor crystal with a strong temperature dependence, the resistance of which is measured to obtain its temperature.
The device is small so it quickly comes into thermal equilibrium with the part of a person it touches. The electric property that impedes current crudely similar to friction and air resistance is called resistance R.
Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current.
Resistance is defined as inversely proportional to current, or. Thus, for example, current is cut in half if resistance doubles. Combining the relationships of current to voltage and current to resistance gives. These include good conductors like copper and aluminum, and some poor conductors under certain circumstances. Ohmic materials have a resistance R that is independent of voltage V and current I. An object that has simple resistance is called a resistor , even if its resistance is small.
Figure 1 shows the schematic for a simple circuit. A simple circuit has a single voltage source and a single resistor. The wires connecting the voltage source to the resistor can be assumed to have negligible resistance, or their resistance can be included in R. Figure 1. A simple electric circuit in which a closed path for current to flow is supplied by conductors usually metal wires connecting a load to the terminals of a battery, represented by the red parallel lines. The zigzag symbol represents the single resistor and includes any resistance in the connections to the voltage source.
What is the resistance of an automobile headlight through which 2. This is a relatively small resistance, but it is larger than the cold resistance of the headlight. As we shall see in Resistance and Resistivity , resistance usually increases with temperature, and so the bulb has a lower resistance when it is first switched on and will draw considerably more current during its brief warm-up period.
Resistances range over many orders of magnitude. Resistance is related to the shape of an object and the material of which it is composed, as will be seen in Resistance and Resistivity. This expression for V can be interpreted as the voltage drop across a resistor produced by the flow of current I. The phrase IR drop is often used for this voltage.
For instance, the headlight in Example 1 above has an IR drop of
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