What is the relationship between voltage and total resistance when a third resistor is added in parallel?

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When a third resistor is added in parallel to a circuit, the total resistance decreases. This occurs because resistors in parallel provide multiple pathways for current to flow. The formula for calculating total resistance (R_total) for resistors in parallel is given by:

[ \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots ]

As more resistors are added in parallel, the reciprocal of the total resistance increases, leading to a reduction in the overall resistance of the circuit. When the total resistance decreases, for a given voltage, the current flowing through the circuit increases according to Ohm's law ((V = IR)). This means that with lower total resistance, the circuit can draw more current from the power source at the same voltage. Therefore, the addition of a third resistor in parallel decreases the total resistance.