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DC Circuits

# Voltage Dividers

Many electrical and electronics equipment use voltages of various levels
throughout their circuitry. One circuit may require a 9-volt supply, another
a 15-volt supply, and still another a 18-volt supply. These voltage
requirements could be supplied by three individual power sources. This method is
expensive and requires a considerable amount of room. The most common method
of supplying these voltages is to use a single voltage source and
a **voltage divider**.

A typical voltage divider consists of two or more resistors connected in
series across a source voltage (*V*_{in}). The source voltage
must be as high or higher than any voltage developed by the voltage divider.
As the source voltage is dropped in successive steps through the series
resistors, any desired portion of the source voltage may be "tapped off" to
supply individual voltage requirements. The values of the series resistors
used in the voltage divider are determined by the voltage and current
requirements of the loads.

Consider the circuit of figure below, which represents a simple voltage
divider. Physically we know that if *V*_{in} is applied to
the input, the output *V*_{R2} will be
less than *V*_{in} because some of *V*_{in} is used
up in forcing current through resistor *R*_{1}. The amount of
voltage used up in *R*_{1} is *V*_{R1}.

Likewise, the voltage appearing across *R*_{2} is *V*_{R2},
the output voltage in this circuit. Now we should like to
find a ready means of determining the voltage across *R*_{2},
which we are calling *V*_{R2}.
(*V*_{in}, *R*_{1} and *R*_{2}
are assumed known.)

By Ohm's law we know that the voltage across a specific resistor is equal to
the current through that resistor multiplied by the ohmic value of the resistor.
In equation form we would write
*V*_{R2} = *I* × *R*_{2}.

Apparently, to evaluate *V*_{R2}, we must first determine *I*.
Recalling that *I* in the simple series circuit shown is

we can then substitute this value of *I* in the original expression
for *V*_{R2} — the first equation above — and obtain

The quantity *R*_{2}/(*R*_{1}+*R*_{2})
is then seen to be the ratio between the output and the input voltages.

If we were interested in the voltage across *R*_{1}, it would be
equal to

If a load resistance is placed across any of the resistors, voltage will be supplied to the load resistance and current will be drawn by it. When current is drawn from the divider, the total current flowing in the circuit will increase because the total resistance of the circuit has decreased.

If the total current flowing in the divider circuit is affected by the loads
placed on it, then the voltage drops of each divider resistor will also be
affected. When a voltage divider is being designed, the maximum current drawn
by the loads will determine the value of the resistors that form the voltage
divider. Normally, the resistance values chosen for the divider will
permit a current equal to ten percent of the total current drawn by the
external loads. This current which does not flow through any of the load
devices is called **bleeder current**.

**Example:**

A simple voltage divider with no load applied is shown in the figure below.

The voltage divider illustrated is composed of two resistors of equal value. Therefore, the voltage drop across each resistance will be the same. The total current flowing in the circuit will be

The potential difference between points (A) and (B) is equal to 50 V. If a resistor is placed between (A) and (B), the voltage drop between these points will be reduced.

The figure above shows the same divider circuit with a load resistor connected. The total resistance may be computed

It can be seen that the total resistance has decreased. This results in a corresponding increase in current flow. Total current is determined as follows

An analysis of the voltage drops shows the following change in the voltage distribution of the circuit

Notice that while the value of the voltage between points (A) and (B) is
reduced the voltage drop across *R*_{1} is increased. The amount
of current flow through the load can be found in this manner

The variation of voltages and currents found in the previous example are undesirable in a voltage divider. It must be designed to provide voltages that are as stable as possible. A voltage divider consisting of two resistors will be designed using the circuit configuration shown in the figure below. The supply voltage is 200 V. It is desired to furnish a voltage of 50 V to the load drawing 6 mA.

Assume bleeder current to be ten percent of the required load current.

Total load current (*I*_{RL}) is specified as 6 mA. The bleeder
current through *R*_{2}, therefore should be

The bleeder current and the current through resistor *R*_{L}
combine and both currents flow through *R*_{1}. This current
value may be computed

The resistance value of *R*_{L} must be as follows

Computing for *R*_{1} and *R*_{2}