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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. 

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