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.
These laws are essential for understanding and calculating electrical circuits,
allowing to predict the behavior of components under different operating conditions.
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.
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
R_{2} and thus, we find the value of the voltage on R_{2}.
Notice how easy it is to calculate a resistive voltage divider. And if we are
interested in calculating the voltage drop over R_{1}? Well, nothing could be simpler.
It would be enough to change the numerator, R_{2} to R_{1}. Easy, right?
The eq. 10-05 show the generalized equation for "n" resistors in series.
Note that the numerator contains R_{2}. In this case, we are calculating
the voltage drop across R_{2}. So, if it were another resistor in the
numerator, for example R_{3}, then we would be calculating the drop in
tension on R_{3}. Of course, in this case we should have a circuit
with at least three resistors in series.
Notice how easy it is to calculate a resistive voltage divider. And if we are
interested in calculating the voltage drop over R_{1}? Well, nothing could be simpler.
It would be enough to change the numerator, R_{2} to R_{1}. Easy, right?
Below we show the generalized equation for "n" resistors in series.
Note that the numerator contains R_{2}. In this case, we are calculating
the voltage drop across R_{2}. So, if it were another resistor in the
numerator, for example R_{3}, then we would be calculating the drop in
tension on R_{3}. 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.
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 R_{3}.
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.
As our objective was to calculate the current through the resistor R_{3}, then in
denominator appears R_{3}. If we want the current in any other resistor
just divide by its respective value.
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
R_{1}. In this case, the value of the resistor that goes in the numerator is R_{2}, 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.
See a practical application of this equation in problem 10-02 Clicking here!