# Why does the overall resistance of a circuit decrease as the resistors are connected in parallel?

The overall resistance of a circuit decreases when resistors are connected in parallel due to the combined effect of providing multiple paths for current flow. In a parallel configuration, each resistor offers a separate path for current to travel from the voltage source to the ground. As more resistors are added in parallel, the total resistance decreases because the effective resistance seen by the voltage source diminishes. This is because the reciprocal of the total resistance in a parallel circuit is equal to the sum of the reciprocals of each individual resistor’s resistance (1/R_total = 1/R1 + 1/R2 + 1/R3 + …). Therefore, adding more parallel branches increases the number of paths through which current can flow, resulting in a lower total resistance.

Resistance decreases when resistors are connected in parallel because each resistor provides an additional path for current to flow. In a parallel circuit, the current divides among the branches according to the inverse of their resistances. This means that the total current drawn from the voltage source increases as more parallel paths are added, resulting in a lower overall resistance. The added paths allow for greater total current flow, which in turn reduces the overall resistance experienced by the entire circuit.

As the number of parallel branches increases in a circuit, the overall resistance of the circuit decreases. This phenomenon occurs because adding more parallel paths provides multiple routes for current to flow from the voltage source to the ground. Each additional path reduces the effective resistance seen by the voltage source, as the total current drawn increases with the availability of more paths. Consequently, the overall resistance decreases proportionally to the number of parallel branches, illustrating how parallel configurations offer lower resistance pathways compared to single paths in series.

When resistors are added in parallel, the total resistance of the circuit decreases. This is because the total resistance in a parallel configuration is less than the resistance of the smallest individual resistor in that configuration. In parallel circuits, the reciprocal of the total resistance is equal to the sum of the reciprocals of each resistor’s resistance. Therefore, the total resistance decreases as more resistors are added in parallel, allowing for greater current flow and reducing the overall resistance seen by the voltage source.

The total resistance of a parallel circuit is less than the resistance of the smallest resistor in that circuit due to the nature of parallel connections. In a parallel configuration, each resistor provides a separate path for current to flow, allowing more current to pass through the circuit than would be possible with a single resistor alone. As a result, the total resistance of the circuit is lower than the resistance of any individual resistor because the combined effect of multiple paths reduces the overall resistance seen by the voltage source. This characteristic makes parallel circuits advantageous for applications requiring lower overall resistance and higher current capacity compared to series configurations.