Voltage Dividers !

Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !
Voltage Dividers !

Loaded Voltage Divider:

 

The voltage divider can be loaded by connecting it to a load (resistor RL in the diagram below). This load resistance conducts a load current IL, while resistor R2 conducts a parallel current IQ. Resistor R1 conducts the sum of these two currents. The parallel current IQ produces heat loss in resistor R2.

For an unloaded voltage divider, the voltage across R2 is proportional to the ratio between R2 and the total resistance R1 + R2. By contrast, a loaded voltage divider exhibits a curved characteristic whose deviation from the linear characteristic in the unloaded state is inversely proportional to the ratio between the load resistance and the total resistance R1 + R2 in the unloaded state, i.e. directly proportional to the ratio between the load current and the parallel current across the divider resistor being loaded. This is because the loaded voltage divider comprises a series connection between R1 and the parallel connection of R2 and RL. The equivalent resistance R2* of this parallel circuit is calculated as follows: 

Accordingly, the voltage divider's load voltage UL is 

The value for the unloaded state is derived by letting the load resistance RL approach infinity. In this case, the resistance R2 is negligible compared with RL in both denominator terms:

RL can then be reduced to result in the equation for an unloaded voltage divider as determined in the previous section. A voltage divider's load voltage is thus always smaller in the loaded state than in the unloaded (idle) state.

Given UL, the currents IL and IQ can be calculated using Ohm's law and the total current I is the sum of these two currents.

The interactive animation below shows a voltage divider which can be connected to a load resistance RL via the button with the red cross. Set different values for the various resistances and observe the resulting effects on voltage and current in the loaded and unloaded states. Note especially how sharply the load voltage UL drops in the loaded state compared with the unloaded state. 

Unloaded Voltage Divider:

 

For the purposes of measurement, it is often necessary to tap sub-voltages from a primary voltage. This is done by means of voltage division. Illustrated below is a voltage divider consisting of two series-connected resistors R1and R2.

Voltage Dividers !

The supply voltage U to the outer terminals and this is then divided into the two sub-voltages U1 and U2. According to the voltage division law,

Voltage Dividers !

According to Ohm's law, the current in the voltage divider is

Voltage Dividers !

and the voltage drop across the two resistors is

Voltage Dividers !

If the expression for current as derived above is substituted into these two equations, the following equations are obtained for the two sub-voltages:

Voltage Dividers !

These equations apply only when no current is being tapped from the voltage divider, i.e. in the no-load state.

The interactive animation below shows a voltage divider whose supply voltage and resistance values can be adjusted with the mouse. If you modify these variables, you will be able to observe the corresponding effects on both sub-voltages.

Voltage Divider with a Potentiometer:

 

In actual practice, use is mainly made of a continuously adjustable voltage divider in the form of a so-called potentiometer. This device has three connections, one of them is a variable sliding contact permitting the potentiometer's total resistance to be divided into two partial resistances R1 and R2. As a result, the output voltage U2 present across the potentiometer's sliding contact can be divided at any point between the full value U (i.e. the value applied to the potentiometer's outer terminals) and zero. The diagrams below illustrate the principle of a potentiometer (left) and its circuit symbol (right).

Voltage Dividers !

Potentiometers are available in a variety of designs such as rotary and sliding formats.  These two designs are illustrated below (left: rotary potentiometer; right: sliding potentiometer).

Voltage Dividers !
The interactive animation below shows a potentiometer whose voltage supply and total resistance are adjustable. The sliding control on the right is used to vary the tapping point for the output voltage U2. Move the tap and observe the resulting effects on the partial resistances and output voltage.

Bridge Circuits​:

 

A bridge circuit consists of two voltage dividers connected in parallel as illustrated below.

Voltage Dividers !

If the upper voltage divider (comprising resistors R1 and R2) divides the supply voltage in the same ratio as the lower voltage divider (comprising resistors R3 and R4), the potential between points C and D is zero (UD = 0). In this state, the bridge is said to be balanced. The balancing condition is

Voltage Dividers !

If resistors R3 and R4 are replaced by an adjustable resistor, the bridge circuit can be used to measure resistances; this kind of circuit is termed Wheatstone bridge after the English physicist of the same name (see the diagram below).

Voltage Dividers !

Rx is the unknown resistance, RN a (usually switchable) standard resistance for comparison. To perform the measurement, the bridge is balanced (UD = 0) and Rx determined using the following relationship:

Voltage Dividers !

 

 

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