What shortcut calculation is used to approximate the total resistance of a circuit that includes several identical devices wired in parallel?

The total resistance of resistors connected in parallel can be approximated using a straightforward calculation. When identical devices are wired in parallel, the total resistance can be determined by taking the resistance of a single device and dividing it by the number of devices in the circuit.

This is because, in a parallel circuit, the total current is the sum of the currents through each device, leading to a situation where the total resistance decreases as more identical devices are added. The formula for total resistance ( R_t ) in a parallel configuration of identical resistors ( R ) is expressed as:

[

R_t = \frac{R}{n}

]

where ( n ) is the number of identical resistors. This means that as you increase the number of parallel branches (devices), the total resistance effectively becomes smaller. Thus, calculating the total resistance involves assessing how much one device contributes to the overall flow of current and effectively scaling this contribution by the number of devices present.