A 4 Ω resistor and a 12 Ω resistor are connected in parallel to a 24 V supply. Find the total resistance.

A 4 Ω resistor and a 12 Ω resistor are connected in parallel to a 24 V supply. Find the total resistance.

• A. 3 Ω
• B. 2 Ω
• C. 4 Ω
• D. 6 Ω

Answer: (A)

In parallel circuits, the total resistance is found by adding the reciprocals of each resistor: 1/R_total = 1/R1 + 1/R2. For 4 Ω and 12 Ω, 1/R_total = 1/4 + 1/12 = 0.25 + 0.0833... = 0.3333..., so R_total = 3 Ω. The total resistance in parallel is always smaller than the smallest individual resistance, which here is 4 Ω, so 3 Ω makes sense. The 24 V supply would give a current of I = V/R_total = 24/3 = 8 A, though the current isn’t needed to find the resistance.

In parallel circuits, the total resistance is found by adding the reciprocals of each resistor: 1/R_total = 1/R1 + 1/R2. For 4 Ω and 12 Ω, 1/R_total = 1/4 + 1/12 = 0.25 + 0.0833... = 0.3333..., so R_total = 3 Ω. The total resistance in parallel is always smaller than the smallest individual resistance, which here is 4 Ω, so 3 Ω makes sense. The 24 V supply would give a current of I = V/R_total = 24/3 = 8 A, though the current isn’t needed to find the resistance.