# When a load is connected to a voltage divider, will the total resistance of the circuit increase or decrease?

Mar 11, 2018

It decreases

#### Explanation:

The load is connected in parallel to one part of the voltage divider - reducing its resistance. This part is in series with the other half of the voltage divider - and thus, the total resistance goes down.

If ${R}_{L}$ is the load resistance which is connected across the part ${R}_{2}$ of a voltage divider consisting of ${R}_{1}$ and ${R}_{2}$, then the total resistance. once the load is connected is

${R}_{1} + \frac{{R}_{2} {R}_{L}}{{R}_{2} + {R}_{L}}$

since the second term is smaller than ${R}_{2}$, this expression is smaller than ${R}_{1} + {R}_{2}$ which is the total resistance without the load.