In a practical voltage divider, when a load is connected across one of the divider's output nodes, how does the total equivalent resistance seen by the source change?

Introduction / Context:
Voltage dividers are widely used to derive lower voltages or reference levels. However, connecting a load across a tap changes the divider's behavior. Understanding how the load alters the total equivalent resistance seen by the source is key to predicting the new currents and voltages (loading effect).

Given Data / Assumptions:

• A two-resistor divider (or multi-resistor ladder) is driven by a source.
• A load resistor RL is connected from the output node to ground (or the lower node).
• All components are linear, and connections are ideal.

Concept / Approach:
When the load is attached, it appears in parallel with the lower divider resistor (or with a segment of the ladder). The parallel combination is always less than or equal to the smallest of the two resistances. Therefore, the total equivalent resistance from the source terminal, which includes that parallel combination, must decrease relative to the unloaded divider.

Step-by-Step Solution:
Let the divider be Rtop in series with Rbottom.Without load: Req_unloaded = Rtop + Rbottom.With load RL across Rbottom: Rbottom_loaded = (Rbottom * RL) / (Rbottom + RL).New total: Req_loaded = Rtop + Rbottom_loaded.Since Rbottom_loaded <= Rbottom, we have Req_loaded <= Req_unloaded.

Verification / Alternative check:
Example: Rtop = 10 kΩ, Rbottom = 10 kΩ. Unloaded Req = 20 kΩ. With RL = 10 kΩ, Rbottom_loaded = 10k||10k = 5 kΩ, so Req_loaded = 15 kΩ, clearly decreased.

Why Other Options Are Wrong:

• Double / increase / remain the same: A parallel addition cannot increase the equivalent resistance or leave it unchanged unless RL is infinite (no load). In normal loading, it decreases.

Common Pitfalls:

• Ignoring loading and assuming the divider ratio is unchanged; output voltage will droop under load.
• Forgetting to compute the parallel combination Rbottom||RL.

Final Answer:
decrease