The Ohm's Law is based on the relation between the three elements that make up a circuit
electric, that is:

Electric Voltage (V), Electric Current (I)
and Electric Resistance (R)

And the relationship between these variables is given by:

eq. 10-01

For this equation to work properly, we must point out that we adopt the conventional sense of the electric current,
this is the current flows from the highest potential to the lowest potential.

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

As a result of this convention, we realize that the sum of the voltage drops on the two resistors of the
circuit must be equal to voltage of the power supply, symbolized by V in the circuit, or:

V = e_{1} + e_{2}

2. Resistive Voltage Divider

One of the commonly used circuits in electricity is the so-called voltage divider resistive.
What does this circuit consist of? It is basically a circuit made up of two or more resistors in series, such that we want to calculate the voltage drop across one or more resistors. See the figure below, where we show two resistors in series and we want to calculate the voltage drop on the resistor R_{2}.

One way of calculating this voltage drop is to first calculate the electric current flowing through the circuit. Subsequently we multiply by the value of R_{2} and thus we find the value of the voltage on R_{2}.

In the circuit of the Figure 10-02
, we call this voltage of V_{ab}. Note that in eq. 10-02
shown in the figure below, we have exactly this calculation. Naturally
V / (R_{1} + R _{2}) is the value of the current circulating in the circuit.
In the numerator of the fraction appears R_{2}. In this way, when we multiply the
electric current circulating in the circuit by the value of R_{2},
we are calculating the value of V_{ab}. But we must realize that (R_{1} + R_{2}) is
equivalent resistance of the circuit. Then we can simplify the equation, or:

eq. 10-02

Notice how easy it is to calculate a resistive voltage divider. And if we are
interested in calculating the voltage drop over R_{1}? It's just simple.
It would suffice to swap in the numerator, R_{2} by R_{1}. Easy, is not it?

In the figure below, the generalized equation for n series resistors appears.
Note that no numerator is R_{2}. In this case, we are calculating
the voltage drop over R_{2}. Thus, if it were another resistor in the
numerator, for example R_{3}, then we would be calculating the
voltage over R_{3}. Of course, in this case, we should have a circuit
with at least three resistors in series.

eq. 10-03

3. Current Divider Resistive

Another frequently used circuit in electricity is the so-called current divider
resistive. What does this circuit consist of? It's basically a circuit made up of
two or more resistors in parallel, in such a way that we want to calculate the electric current
which circulates through a given circuit resistor.
See the Figure 10-03 where we are showing three resistors
in parallel and we want to calculate the electric current on the resistor R_{3}.

Note the fact that in a parallel circuit the electrical voltage is the same
on any resistor in the circuit. In this way, this voltage is the product between the
total electric current that circulates in the circuit and equivalent resistance
of the parallel.

Therefore, to calculate the current in any resistor simply divide the voltage by
the value of the resistor. This is what the equation below shows. In this equation,
we have the product I R_{eq} represents the voltage at which the resistor
R_{3} is submitted.

eq. 10-04

As our goal was to calculate the current through the resistor R_{3}, then
denominator appears R_{3}. If we want the current in any other resistor
just divide by their respective value.