In a parallel connection, what is true about the total resistance?

In a parallel connection, the total resistance is indeed less than the smallest individual resistance in the circuit. This behavior occurs because when resistances are connected in parallel, the current has multiple paths to flow through. Each additional path decreases the overall resistance of the circuit.

The formula for total resistance ( R_t ) in a parallel circuit is given by:

[ \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots ]

This means that as more resistors are added in parallel, their combined effect spreads out the current across multiple paths, thereby reducing the total resistance.

When comparing the total resistance to the smallest resistance in the arrangement, you can understand that since each parallel resistor provides an alternative pathway for current, the total resistance decreases. Therefore, it cannot be greater than or equal to the smallest resistance; it must be less than it.

The other statements do not hold true in a parallel circuit, where the total resistance cannot be equal to the largest resistance, equal to the sum of all resistances, or always zero, because the values of the individual resistances must be taken into