Which is correct concerning a parallel circuit?

Which is correct concerning a parallel circuit?

• A. Total resistance will be smaller than the smallest resistor
• B. Total resistance will be larger than the largest resistor
• C. Total resistance equals the sum of the resistors
• D. Total resistance equals the largest resistor

Answer: (A)

In a parallel circuit, each resistor provides a separate path for current, so the overall resistance drops. The combined resistance follows 1/R_total = 1/R1 + 1/R2 + ...; this means R_total is always smaller than the smallest individual resistor. For example, 4 Ω and 6 Ω in parallel give R_total = (4×6)/(4+6) = 2.4 Ω, which is less than both 4 Ω and 6 Ω. Adding more parallel paths continues to lower the total resistance. This is why the total is not the sum of the resistances (that would be a series case) and not the largest resistor. It’s also not larger than the largest resistor because every additional parallel path provides another route for current, reducing the overall resistance.

In a parallel circuit, each resistor provides a separate path for current, so the overall resistance drops. The combined resistance follows 1/R_total = 1/R1 + 1/R2 + ...; this means R_total is always smaller than the smallest individual resistor. For example, 4 Ω and 6 Ω in parallel give R_total = (4×6)/(4+6) = 2.4 Ω, which is less than both 4 Ω and 6 Ω. Adding more parallel paths continues to lower the total resistance.

This is why the total is not the sum of the resistances (that would be a series case) and not the largest resistor. It’s also not larger than the largest resistor because every additional parallel path provides another route for current, reducing the overall resistance.