In a parallel network, the total resistance is less than the smallest resistor.

In a parallel network, the total resistance is less than the smallest resistor.

• A. Greater than the largest resistor
• B. Equal to the largest resistor
• C. Less than the smallest resistor
• D. Equal to the smallest resistor

Answer: (C)

In a parallel network, current has multiple paths, so the overall conductance increases. The total resistance is found from 1/R_total = sum of 1/R_i. Since you’re adding positive terms, the sum is larger than the conductance of any single resistor, which means R_total must be smaller than each individual resistor value—especially smaller than the smallest one. For example, two resistors in parallel, 6 ohms and 3 ohms, give 1/R_total = 1/6 + 1/3 = 1/2, so R_total = 2 ohms, which is less than both 6 and 3. So the total resistance in a parallel circuit with more than one resistor is less than the smallest resistor. This wouldn’t be the case if there were only a single resistor, in which case the total equals that resistor.

In a parallel network, current has multiple paths, so the overall conductance increases. The total resistance is found from 1/R_total = sum of 1/R_i. Since you’re adding positive terms, the sum is larger than the conductance of any single resistor, which means R_total must be smaller than each individual resistor value—especially smaller than the smallest one. For example, two resistors in parallel, 6 ohms and 3 ohms, give 1/R_total = 1/6 + 1/3 = 1/2, so R_total = 2 ohms, which is less than both 6 and 3.

So the total resistance in a parallel circuit with more than one resistor is less than the smallest resistor. This wouldn’t be the case if there were only a single resistor, in which case the total equals that resistor.