Ohm's Law theory and study

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2. - Ohm's Law clique aqui!

3. - Resistive Voltage Divider clique aqui!

4. - Resistive Current Divider clique aqui!

2. Ohm's Law

Ohm's Law

Ohm's first law

eq. 10-01

eq. 10-01

Where the meaning of the variables are:

V - is the electrical voltage, measured in volts
I - is the electric current, measured in amperes
R - is the electrical resistance, measured in ohms

Ohm's second law relates the resistance of a material with its physical properties and resistivity, which is a characteristic of the material. This law is expressed by eq. 10-02.

eq. 10-02

Where the meaning of the variables are:

R - is the electrical resistance, measured in ohms
ρ - is the electrical resistivity of the material, measured in ohms.meter
A - is the cross-sectional area of the conductor, measured in meter²
L - is the length of the conductor, measured in meter

These laws are essential for understanding and calculating electrical circuits, allowing to predict the behavior of components under different operating conditions.

Figure 10-01

Ohm's Law

Note in Figure 10-01, that the direction of current in the circuit is indicated by green arrow and the polarity of the voltage drop across the resistors, by the signs + and - . On the resistor side where the current enters will always be the positive polarity of the drop tension on it.

Kirchhoff's Law

chapter 13

Kirchhoff's voltage law

eq. 10-03

eq. 10-03

3. Resistive Voltage Divider

resistive voltage divider

Figure 10-02

R₂

One of the ways to calculate this voltage drop is, first, to calculate the current electricity flowing through the circuit. Afterwards, we multiply by the value of R₂ and thus, we find the value of the voltage on R₂.

V_ab

eq. 10-04

V/ (R₁ + R₂)

R₂

V_ab

(R₁ + R₂)

equivalent resistance

eq. 10-04

Notice how easy it is to calculate a resistive voltage divider. And if we are interested in calculating the voltage drop over R₁? Well, nothing could be simpler. It would be enough to change the numerator, R₂ to R₁. Easy, right?

The eq. 10-05 show the generalized equation for "n" resistors in series. Note that the numerator contains R₂. In this case, we are calculating the voltage drop across R₂. So, if it were another resistor in the numerator, for example R₃, then we would be calculating the drop in tension on R₃. Of course, in this case we should have a circuit with at least three resistors in series.

eq. 10-05

Below we show the generalized equation for "n" resistors in series. Note that the numerator contains R₂. In this case, we are calculating the voltage drop across R₂. So, if it were another resistor in the numerator, for example R₃, then we would be calculating the drop in tension on R₃. Of course, in this case we should have a circuit with at least three resistors in series.

This type of circuit is widely used in electronics to create specific voltage levels required for sensitive components, such as sensors and microcontrollers, ensuring that they receive the appropriate voltage for their correct operation. Additionally, voltage dividers are used for voltage measurements as they allow higher voltages to be safely measured by instruments that cannot measure high voltages. On the other hand, Voltage dividers are useful for reading analog voltage levels on microcontrollers, such as the Arduino, where the input voltage Divider output can be mapped to a corresponding digital value.

In summary, the resistive voltage divider is a versatile tool to use, allowing adaptation of voltages for a wide range of applications, ensuring the safety and efficiency of electronic components.

4. Resistive Current Divider

Another frequently used circuit in electricity is the so-called resistive current divider . What does this circuit consist of? Basically it is a circuit formed by two or more resistors in parallel, such that we want to calculate the electric current that circulates through a given resistor in the circuit. See Figure 10-03 where we are showing three resistors in parallel and we want to calculate the electric current through the resistor R₃.

Pay attention to the fact that in a parallel circuit the electrical voltage is the same on any resistor in the circuit. This is a fundamental characteristic of parallel circuits and differs from series circuits, where the voltage is divided between the components. Thus, this tension is the product between total electrical current flowing in the circuit and the equivalent resistance of the parallel.

eq. 10-06

I R_eq

R₃

eq. 10-06

As our objective was to calculate the current through the resistor R₃, then in denominator appears R₃. If we want the current in any other resistor just divide by its respective value.

Observação

If the circuit has only two resistors in parallel, the eq. 10-06 can be simplified. Suppose we are interested in calculate the current flowing through R₁. In this case, the value of the resistor that goes in the numerator is R₂, that is, the resistor where we do not have interest in calculating the current. And the sum of the two resistors is placed in the denominator. See eq.10-07 for further clarification.

eq. 10-07

See a practical application of this equation in problem 10-02 Clicking here!

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