Mathematics

Applying Ohms Law to Simple Resistive Circuits



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Ohm’s law is one of the most fundamental laws to keep in mind when analyzing an electrical circuit. How, then, does one go about applying it? Before using Ohm’s law, it is necessary to understand the three concepts that the law relates to one another.

1. Current

Currents are observed in several aspects of daily life; wind is a current of air and ocean currents are currents of water. Just like ocean currents are movements of water, electric currents are simply the movement of electrically charged particles such as electrons. The motion of these particles is used to drive the operation of modern devices similarly to the way that water currents can be used to power mills. Electric current is measured in amperes, or amps for short. If one amp is flowing in a wire, it means that every second one coulomb, which is about 6 billion billions of electrons, passes through the wire.

2. Voltage

Voltage is what causes electric currents to flow. It can be thought of as electrical “pressure” because it pushes electrons through a circuit. Returning to the water analogy, in the same way that high pressures cause water to flow to lower pressures, high voltages cause electrons to flow to lower voltages. Voltage is measured in units of volts.

3. Resistance

Resistance is a property of an object that determines how difficult it is for electric current to flow through an object. The electrical component that gives a circuit resistance is called a resistor. A resistor has a wire on either end and makes it difficult for current to flow from what is connected at one end of the resistor to what is connected at the other end of the resistor.

In the water analogy, a resistor is analogous to a narrow pipe or funnel that the water must go through. Imagine a bucket and a 2-liter soda bottle each filled with water. If the bucket were turned upside-down, all of the water would flow out very quickly. If the soda bottle were flipped over, the water would take a much longer time to flow out. This is because the narrow opening at the top of the soda bottle introduces a high resistance. Just like the neck of the bottle slows down water flowing from a soda bottle, a resistor with a high resistance slows down the electrons in a circuit more, resulting in a lower current.

Resistance is measured in ohms. An ohm is the resistance through which a voltage difference of one volt could push one amp.

-Ohm’s law

With these three concepts defined, it is now possible to understand Ohm’s law. Ohm’s law describes how much current will flow through a resistor when the voltage on either side of the resistor is different. The law says that the amount of current that flows in a resistor is equal to the difference between the voltages at either end of the resistor divided by the resistance, or in equation form, I = V/R (I is the symbol used for current, V is used for voltage and R is used for resistance). Moreover, the law also states that current will flow from the higher voltage to the lower voltage.

For example, if the positive end of a 10-volt source is connected to the left end of a 2 ohm resistor, and the negative end of the source is connected to the right end of the resistor, it is straightforward to determine how much current is flowing through the resistor. The source provides a voltage difference of 10 volts, and the resistance is 2 ohms. Dividing these two quantities shows that a current of 5 amps flows from the left to the right end of the resistor (because the left end is connected to the positive voltage). Charges continue to flow through the resistor at a rate of 2 coulombs per second (from the definition of the ampere) until the voltage difference is removed.

-Series and parallel resistances

Ohm’s law describes the current flowing through a single resistor, but what if current is flowing through a network of resistors? In this case, the amount of current flowing into and out of the network can be found using the concepts of series and parallel resistances. These ideas can be used to simplify a complicated network of resistors to a single resistance, to which Ohm’s law can be applied.

Two resistors are in series if one end of the first resistor is connected to one end of the second resistor. That is, if charges leaving one resistor have nowhere to go but into the second resistor. These resistors will behave exactly the same as one resistor whose resistance is the sum of the two real resistances. So, if a 2 ohm resistor is in series with a 3 ohm resistor, and a 15 volt difference is applied across the combination of resistors, the resistors will behave the same as a single 5 ohm resistor (because 2+3=5), allowing 3 amps to flow through the series of resistors.

Two resistors are in parallel if one end of the first resistor is connected to one end of the second resistor, and the opposite ends are connected to each other as well. In this situation, current can flow through either resistor and will end up at the same point regardless of which resistor it flows through. These resistances are equivalent to a resistance determined using the reciprocal-sum formula. For two resistors in parallel, first add the reciprocals of the resistances, and then take the reciprocal of the result. For example, if a 3 ohm and a 6 ohm resistor are connected in parallel, then they are equivalent to a single 2 ohm resistor. This is because the reciprocals are 1/3 and 1/6, which when added together are 3/6. The reciprocal of 3/6 is 6/3, or 2 ohms.

These concepts may be combined. For instance, a parallel combination of resistors may be in series with a third resistor. In order to calculate the so called equivalent resistance, first find the equivalent resistance of the parallel resistors, and then add that to the third resistor. Once this network has been simplified to a single resistance, Ohm’s law can be applied to determine the current flowing through the network.

A proper understanding of Ohm’s law and the concepts of series and parallel resistances will make it possible to calculate the current flowing in almost any simple circuit consisting of sources and resistors, and will provide a strong foundation upon which to build further electric circuit analysis skills.

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  • InfoBoxCallToAction ActionArrowhttp://www.osv.org/explore_learn/waterpower/sawmill.html
  • InfoBoxCallToAction ActionArrowhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/watcir.html