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# Loaded Voltage Divider

The voltage divider can be loaded by connecting it to a load (resistor *R*_{L }in the diagram below). This load resistance conducts a load current *I*_{L}, while resistor *R*_{2} conducts a parallel current *I*_{Q}. Resistor *R*_{1} conducts the sum of these two currents. The parallel current *I*_{Q} produces heat loss in resistor *R*_{2}.

For an unloaded voltage divider, the voltage across *R*_{2} is proportional to the ratio between *R*_{2} and the total resistance *R*_{1} + *R*_{2}. 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 *R*_{1} + *R*_{2} 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 *R*_{1} and the parallel connection of *R*_{2} and *R*_{L}. The equivalent resistance *R*_{2}^{*} of this parallel circuit is calculated as follows:

Accordingly, the voltage divider's load voltage *U*_{L} is

The value for the unloaded state is derived by letting the load resistance *R*_{L} approach infinity. In this case, the resistance *R*_{2} is negligible compared with *R*_{L} in both denominator terms:

*R*_{L} 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 U_{L}, the currents I_{L} and I_{Q} 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 R_{L} 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 U_{L} drops in the loaded state compared with the unloaded state.*