Electricity and its properties have many times troubled and challenged human knowledge and understanding. The flow of electricity, being bound in space-time to the force of magnetism through maxwell’s equations, is now understood to the point that it can be analyzed and controlled. In this article, we will consider some basic applications of Ohm’s law – the law of electrical resistance. A strong knowledge of this law is imperative if even basic circuits are to be constructed.
Section 1.0 – Definition and Equations
Ohm’s law is defined as follows:
V=IR
Where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. This simple relationship applies when considering any system of resistors in circuits. However, the method through which it applies varies as the situation varies.
Section 2.0 – Resistors in Series
Resistors that are wired in series have a total resistance that is equal to the sum of the resistance of each individual resistor. This relationship can be expressed as follows:
R(total) = R(1) + R(2) + R(3) + … + R(n), where R(n) is the final resistor in the series. This relationship can be applied to questions such as the example that follows:
Two 1 ohm resistors are wired in series. What is the total resistance?
In this case, R(1) = 1 ohm and R(2) = 1 ohm. Therefore, R(total) is equal to 1 + 1 = 2 ohms.
Section 3.0 – Resistors in Parallel
Resistors can be wired in parallel as well as in series. In a parallel arrangement, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistance of each successive resistor. This can be applied to a similar problem as in Section 2.0:
Two 1 ohm resistors are wired in parallel. What is the total resistance?
This works out to 1/2 ohm, as the reciprocal of 1 is one, and the reciprocal of 2 is 1/2.
Let’s take a look at another parallel-series resistor problem. A circuit consists of 3 resistors, a 10 ohm resistor, a 50 ohm resistor, and a 20 ohm resistor. Find the total resistance in series and in parallel configuration.
In series:
R(total) = R(1) + R(2) + R(3)
R(total) = 10ohm + 50ohm + 20ohm
R(total) = 80ohm
In parallel:
1/R(total) = 1/R(1) + 1/R(2) + 1/R(3)
1/R(total) = 1/10 ohm + 1/50 ohm + 1/20 ohm
1/R(total) = 0.1 + 0.02 + 0.05
1/R(total) = 0.17 ohm
R(total) = 5.88 ohm
Conclusion
These are the basic principles of ohm’s law. A good knowledge of its uses and applications is sure to guarantee success in physics and of course in the field of electrical engineering and many other forms of engineering and design. I wish you the best in all of your ohm’s law endeavours!
