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# 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 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.

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 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}