Heating, Ventilation, and Air Conditioning (HVAC ) Electrical Practice Test

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What is the total resistance of a parallel circuit compared to the smallest resistor?

  1. Equal to the smallest resistance

  2. Greater than the smallest resistance

  3. Less than the smallest resistance

  4. Always zero

The correct answer is: Less than the smallest resistance

In a parallel circuit, the total resistance is always less than the smallest resistor in the circuit. This is a fundamental principle of parallel resistance. When resistors are connected in parallel, the overall path for current increases, allowing more current to flow through the circuit compared to a single resistor. Mathematically, the formula for total resistance (R_total) in a parallel circuit is given by: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn Where R1, R2, R3, ..., Rn are the individual resistances. From this equation, you can see that adding more resistors (even if they have higher values) in parallel will result in a total resistance that is reduced to a value less than that of the smallest resistor present. This phenomenon occurs because the paths for current to flow multiply, thus enhancing the overall conductivity of the circuit. Therefore, the total resistance will always be less than the smallest resistor in the parallel configuration, reinforcing why this is the correct choice.

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