In a parallel circuit, how does the total resistance compare to the individual resistances?

In a parallel circuit, how does the total resistance compare to the individual resistances?

• A. Less than the smallest resistance
• B. Equal to the largest resistance
• C. Greater than the sum of resistances
• D. Twice the smallest resistance

Answer: (A)

In a parallel circuit, the total resistance is determined by the fact that currents have multiple paths to flow through. The combined conductance increases because you sum the conductances of each path, so the overall resistance drops. Mathematically, 1/R_total = 1/R1 + 1/R2 + ...; since all terms are positive, the sum is larger than any single 1/Ri, which makes R_total smaller than every individual resistor. For example, two equal resistors of 4 ohms in parallel give R_total = 2 ohms, which is less than the smallest resistor. Adding more parallel paths lowers the total resistance even further. This is why the total resistance in parallel is less than the smallest individual resistance.

In a parallel circuit, the total resistance is determined by the fact that currents have multiple paths to flow through. The combined conductance increases because you sum the conductances of each path, so the overall resistance drops. Mathematically, 1/R_total = 1/R1 + 1/R2 + ...; since all terms are positive, the sum is larger than any single 1/Ri, which makes R_total smaller than every individual resistor. For example, two equal resistors of 4 ohms in parallel give R_total = 2 ohms, which is less than the smallest resistor. Adding more parallel paths lowers the total resistance even further. This is why the total resistance in parallel is less than the smallest individual resistance.