What is the equivalent resistance of four 1000-ohm resistors connected in parallel?

What is the equivalent resistance of four 1000-ohm resistors connected in parallel?

• A. 1000 ohm
• B. 250 ohm
• C. 4000 ohm
• D. 1250 ohm

Answer: (B)

When resistors are in parallel, the total resistance decreases because the current has more paths to flow through. The relationship is 1/R_eq = 1/R1 + 1/R2 + 1/R3 + 1/R4. For four identical resistors of 1000 ohms each, this becomes 1/R_eq = 1/1000 + 1/1000 + 1/1000 + 1/1000 = 4/1000 = 1/250, so R_eq = 250 ohms. You can also think in terms of conductance: each resistor has G = 1/1000 = 0.001 siemens, four in parallel give G_total = 0.004 S, and R_eq = 1/G_total = 250 ohms. This aligns with the shortcut for identical resistors in parallel: R_eq = R/n, which is 1000/4 = 250 ohms.

When resistors are in parallel, the total resistance decreases because the current has more paths to flow through. The relationship is 1/R_eq = 1/R1 + 1/R2 + 1/R3 + 1/R4. For four identical resistors of 1000 ohms each, this becomes 1/R_eq = 1/1000 + 1/1000 + 1/1000 + 1/1000 = 4/1000 = 1/250, so R_eq = 250 ohms. You can also think in terms of conductance: each resistor has G = 1/1000 = 0.001 siemens, four in parallel give G_total = 0.004 S, and R_eq = 1/G_total = 250 ohms. This aligns with the shortcut for identical resistors in parallel: R_eq = R/n, which is 1000/4 = 250 ohms.