Cecily Zamora
Ohm's Law states that the current (I), in amperes, is proportional to the voltage (V), in volts, divided by the impedance (Z), in ohms. In other words, the current is directly proportional to the voltage and inversely proportional to the resistance. This means that if the voltage increases and the resistance remains constant, the current will increase. Likewise, if the resistance in a circuit increases and the voltage remains the same, the current will decrease. However, in real-world applications, resistance can change due to various factors, such as temperature or the presence of inductive reactance or capacitive reactance in the circuit. For example, a heater's resistance changes dramatically when it heats up, affecting the power output. Understanding these factors that influence resistance helps us predict and control the behaviour of electrical circuits, ensuring the safe and efficient operation of electrical devices.
| Characteristics | Values |
|---|---|
| Current | Inversely proportional to resistance |
| Voltage | Directly proportional to current |
| Resistance | Depends on the material and temperature |
| Impedance | Must be included in Ohm's Law if inductive or capacitive reactance is present in the circuit |
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What You'll Learn
Voltage changes
For example, if you have a fixed resistance that is constant, when the voltage is different, the power will also be different. This is because, with a constant resistance, voltage and current will always change simultaneously and in the same ratios. So, if you move to a new country where the power grid output is different, the voltage will change, and the current will change along with it, resulting in a different power.
Additionally, some materials have a resistance that increases as they heat up. For instance, a hairdryer's heating element may have a higher resistance when used in a country with a lower voltage to avoid burning out. This change in resistance due to temperature is another example of why real resistors do not have a single constant resistance value.
Ohm's Law also applies when there is inductive or capacitive reactance in a circuit. In these cases, the law includes the total impedance in the circuit. When there is inductance, the voltage and current are out of phase, with the voltage reaching its maximum value before the current.
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Electric potential
Mathematically, electric potential (V) is defined as the electric potential energy per unit charge, given by the equation V = W/q, where W is the work done and q is the charge. The unit of measurement for electric potential is joules per coulomb (J/C), which is equivalent to a volt (V).
The concept of electric potential is closely related to the idea of potential energy. The potential energy of a charge in an electric field depends on its position within the field. When a positive charge moves against an electric field, its potential energy increases, while its potential energy decreases when it moves with the electric field. For a negative charge, the opposite is true.
It's important to note that only differences in potential energy are measurable. In practical terms, this means that the electric potential at the reference point, typically Earth or a point at infinity, is considered zero. The work done in moving a unit charge from one point to another within an electric circuit is equal to the difference in potential energies at those points. This difference in potential energy can be measured using a voltmeter.
The behaviour of electric potential in the presence of time-varying magnetic fields is more complex. In such cases, the electric field cannot be described solely as a scalar potential but must also include the magnetic vector potential. This combination of scalar and vector potentials forms a four-vector that transforms together under Lorentz transformations.
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Current fluctuations
Ohm's Law, which states that voltage is equal to the current multiplied by the resistance ($V=IR$), is a common material property. It is not a fundamental law of physics, and it does not apply universally. For instance, it does not apply to condensed matter.
In ideal conditions, resistance ($R$) is constant and independent of voltage ($V). However, in reality, resistance can change depending on various factors. For example, the resistance of a heating element in a hairdryer increases as its temperature increases. This change in resistance due to temperature is an example of why resistors do not have a single "R" value.
Fluctuations in current can also cause changes in resistance. Heat increases a resistor's resistance or decreases its conductance, and current decreases when resistance is increased. This creates a cycle where lower current leads to less heat dissipation, which drops the resistance and causes more current to flow, and so on.
In real circuits, however, this fluctuation is not usually observed. As current begins to flow, the resistor will heat up, but it will eventually reach an equilibrium point where the heat generated by the current is matched by the heat radiated into the surrounding air. At this point, the temperature, resistance, and current all remain stable.
The fluctuation effect can be observed in some cases, such as in PTC thermistors, which can reach an equilibrium temperature and require a phase shift or delay to create an oscillator. Additionally, lower heat capacity can lead to oscillations, with heat conductivity determining whether the system is damped or diverged.
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Impedance in the circuit
Impedance is a measure of the total opposition that a circuit or a part of a circuit presents to electric current. It is denoted by the symbol Z and is measured in ohms. Impedance includes both resistance and reactance. The resistance component arises from collisions of the current-carrying charged particles with the internal structure of the conductor. The reactance component is an additional opposition to the movement of electric charge that arises from the changing magnetic and electric fields in circuits carrying alternating current. Impedance reduces to resistance in circuits carrying steady direct current.
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals to the complex representation of the current flowing through it. In general, it depends upon the frequency of the sinusoidal voltage. Impedance extends the concept of resistance to alternating current (AC) circuits and possesses both magnitude and phase, unlike resistance, which has only magnitude.
The unit of impedance, like that of resistance, is the ohm. Depending on the nature of the reactance component of the impedance (whether predominantly inductive or capacitive), the alternating current either lags or leads the voltage. The reciprocal of the impedance, 1/Z, is called the admittance and is expressed in terms of the unit of conductance, the mho unit (ohm spelled backward).
Impedance in an AC system is still measured in ohms and represented by the equation Z = V/I, but V and I are frequency-dependent. In general, neither impedance nor admittance can vary with time, since they are defined for complex exponentials in which −∞ < t < +∞. However, many components and systems may exhibit non-linear or time-varying voltage-to-current ratios that seem to be linear time-invariant (LTI) for small signals and over small observation windows, so they can be roughly described as if they had a time-varying impedance.
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Temperature changes
The influence of temperature on resistance can be understood through the lens of the conductor's geometry and composition. For instance, the resistance of a conductor is influenced by its length and cross-sectional area, with longer and thinner conductors offering greater resistance. Additionally, the material of the conductor plays a crucial role. Conductors with high electrical conductivity, such as metals, tend to have lower resistance at lower temperatures. However, as temperature rises, their resistance increases due to the increased vibrational motion of atoms and molecules impeding the flow of electrons.
It is important to note that the relationship between temperature and resistance is not always linear. While resistance generally increases with temperature, some materials, like silicon, exhibit a negative temperature coefficient of resistivity, meaning their resistance decreases as temperature rises. This behaviour can be attributed to the unique electronic properties of these materials. By combining materials with positive and negative temperature coefficients, it is possible to create a composite resistor whose overall resistance remains relatively stable across different temperatures.
The impact of temperature on resistance is a critical consideration in electrical engineering and circuit design. For example, in a hairdryer, the heating element's resistance may increase as it heats up, leading to a reduction in power consumption. This phenomenon, where resistance changes with temperature, is one of the reasons why real resistors do not exhibit a single, constant resistance value. Understanding how temperature affects resistance is essential for ensuring the safe and efficient operation of electrical devices across varying environmental conditions.
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Frequently asked questions
Ohm's Law states that the current (I), in amperes, is proportional to the voltage (V), in volts, divided by the impedance (Z), in ohms.
According to Ohm's Law, an increase in voltage will result in an increase in current as long as the resistance remains constant. If the voltage remains constant and resistance increases, the current will decrease.
Yes, if you travel to a country with a different power grid output, the voltage will change, and this will affect the resistance. For example, a hairdryer with a certain resistance in one country will have a different resistance in another country with a different voltage.
