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

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

• A. It is greater than the largest resistance
• B. It is equal to the largest resistance
• C. It is less than the smallest resistance
• D. It equals the sum of resistances

Answer: (C)

When resistors are in parallel, the circuit offers multiple paths for current, so the overall resistance drops. The math behind this is 1/R_total = sum of 1/R_i, which means adding more paths increases the total conductance and reduces R_total. In fact, R_total is always less than the smallest individual resistance because the extra path carries some current that would otherwise have to pass through the smallest resistor alone. For example, 4 ohms in parallel with 12 ohms gives 1/R_total = 1/4 + 1/12 = 1/3, so R_total = 3 ohms, which is smaller than 4 ohms. So the total resistance is less than the smallest resistance.

When resistors are in parallel, the circuit offers multiple paths for current, so the overall resistance drops. The math behind this is 1/R_total = sum of 1/R_i, which means adding more paths increases the total conductance and reduces R_total. In fact, R_total is always less than the smallest individual resistance because the extra path carries some current that would otherwise have to pass through the smallest resistor alone. For example, 4 ohms in parallel with 12 ohms gives 1/R_total = 1/4 + 1/12 = 1/3, so R_total = 3 ohms, which is smaller than 4 ohms. So the total resistance is less than the smallest resistance.