A 15 V source powers two resistors in parallel: 30 Ω and 60 Ω. What is the total resistance?

A 15 V source powers two resistors in parallel: 30 Ω and 60 Ω. What is the total resistance?

• A. 30 Ω
• B. 60 Ω
• C. 10 Ω
• D. 20 Ω

Answer: (D)

When resistors are connected in parallel, the same voltage is across each branch, and the total resistance comes from adding their conductances (reciprocals of resistance). So you add 1/R for each resistor to get 1/R_total. Compute 1/R_total = 1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20, which gives R_total = 20 Ω. This total is smaller than either individual resistor, which is a hallmark of parallel connections. If a 15 V source is across the combination, the total current is 15/20 = 0.75 A, with 0.5 A through the 30 Ω branch and 0.25 A through the 60 Ω branch, confirming the calculation since 0.5 + 0.25 = 0.75 A. Therefore the total resistance is 20 Ω.

When resistors are connected in parallel, the same voltage is across each branch, and the total resistance comes from adding their conductances (reciprocals of resistance). So you add 1/R for each resistor to get 1/R_total.

Compute 1/R_total = 1/30 + 1/60 = 2/60 + 1/60 = 3/60 = 1/20, which gives R_total = 20 Ω.

This total is smaller than either individual resistor, which is a hallmark of parallel connections. If a 15 V source is across the combination, the total current is 15/20 = 0.75 A, with 0.5 A through the 30 Ω branch and 0.25 A through the 60 Ω branch, confirming the calculation since 0.5 + 0.25 = 0.75 A. Therefore the total resistance is 20 Ω.