What is the equivalent resistance of three 30 Ω resistors in parallel?

What is the equivalent resistance of three 30 Ω resistors in parallel?

• A. 90 Ω
• B. 30 Ω
• C. 60 Ω
• D. 10 Ω

Answer: (D)

When resistors are in parallel, the total resistance is found by adding the conductances: 1/R_eq = 1/R1 + 1/R2 + 1/R3. For three identical resistors of 30 ohms, that becomes 1/R_eq = 1/30 + 1/30 + 1/30 = 3/30 = 1/10. Therefore, R_eq = 10 ohms. In parallel, adding more paths increases how easily current can flow, so the overall resistance drops. For identical resistors in parallel, you can think of it as R_eq = R/n, which here is 30/3 = 10 ohms. This also contrasts with a series arrangement, where the resistances would simply add to 90 ohms.

When resistors are in parallel, the total resistance is found by adding the conductances: 1/R_eq = 1/R1 + 1/R2 + 1/R3. For three identical resistors of 30 ohms, that becomes 1/R_eq = 1/30 + 1/30 + 1/30 = 3/30 = 1/10. Therefore, R_eq = 10 ohms.

In parallel, adding more paths increases how easily current can flow, so the overall resistance drops. For identical resistors in parallel, you can think of it as R_eq = R/n, which here is 30/3 = 10 ohms. This also contrasts with a series arrangement, where the resistances would simply add to 90 ohms.