When resistors are connected in parallel, does the equivalent resistance increase or decrease relative to the smallest resistor?

When resistors are connected in parallel, does the equivalent resistance increase or decrease relative to the smallest resistor?

• A. Increase
• B. Stay the same
• C. Cannot be determined
• D. Decrease

Answer: (D)

When resistors are connected in parallel, there are multiple paths for current to flow. The overall or equivalent resistance is found using 1/R_eq = 1/R1 + 1/R2 + ... . Because each term 1/R_i is positive, adding more resistors in parallel increases the total conductance (the sum of the reciprocals), which makes 1/R_eq larger and thus R_eq smaller than any individual resistor in the network. For example, if you have a 4-ohm resistor in parallel with an 8-ohm resistor, the combined resistance is 1/R_eq = 1/4 + 1/8 = 3/8, so R_eq = 8/3 ≈ 2.67 ohms, which is less than the smallest resistor (4 ohms). This pattern holds as you add more parallel branches—the equivalent resistance continues to decrease, approaching zero if you add many very small resistances, though it never goes negative. Therefore, the equivalent resistance decreases relative to the smallest resistor.

When resistors are connected in parallel, there are multiple paths for current to flow. The overall or equivalent resistance is found using 1/R_eq = 1/R1 + 1/R2 + ... . Because each term 1/R_i is positive, adding more resistors in parallel increases the total conductance (the sum of the reciprocals), which makes 1/R_eq larger and thus R_eq smaller than any individual resistor in the network.

For example, if you have a 4-ohm resistor in parallel with an 8-ohm resistor, the combined resistance is 1/R_eq = 1/4 + 1/8 = 3/8, so R_eq = 8/3 ≈ 2.67 ohms, which is less than the smallest resistor (4 ohms). This pattern holds as you add more parallel branches—the equivalent resistance continues to decrease, approaching zero if you add many very small resistances, though it never goes negative. Therefore, the equivalent resistance decreases relative to the smallest resistor.