Which formula expresses the relationship for parallel resistances?

Which formula expresses the relationship for parallel resistances?

• A. Req = R1 + R2 + R3
• B. Req = 1/(1/R1 + 1/R2 + 1/R3)
• C. Req = R1 * R2
• D. 1/Req = 1/R1 + 1/R2 + 1/R3

Answer: (D)

When resistors are connected in parallel, the voltage across each one is the same, while the currents through them add up. Using Ohm’s law, the total current is I = V/R1 + V/R2 + V/R3. The equivalent resistance Req is the total voltage divided by the total current, so Req = V / [V(1/R1 + 1/R2 + 1/R3)] = 1 / (1/R1 + 1/R2 + 1/R3). This shows the key relationship: the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances. It’s often handy to rearrange that into Req = 1 / (1/R1 + 1/R2 + 1/R3), which is just another way to express the same idea. For a quick check, if R1 = 6 Ω, R2 = 3 Ω, and R3 = 2 Ω, then 1/Req = 1/6 + 1/3 + 1/2 = 1, so Req = 1 Ω, which is smaller than any individual resistor. The series case would add the resistances, not use reciprocals.

When resistors are connected in parallel, the voltage across each one is the same, while the currents through them add up. Using Ohm’s law, the total current is I = V/R1 + V/R2 + V/R3. The equivalent resistance Req is the total voltage divided by the total current, so Req = V / [V(1/R1 + 1/R2 + 1/R3)] = 1 / (1/R1 + 1/R2 + 1/R3). This shows the key relationship: the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances. It’s often handy to rearrange that into Req = 1 / (1/R1 + 1/R2 + 1/R3), which is just another way to express the same idea. For a quick check, if R1 = 6 Ω, R2 = 3 Ω, and R3 = 2 Ω, then 1/Req = 1/6 + 1/3 + 1/2 = 1, so Req = 1 Ω, which is smaller than any individual resistor. The series case would add the resistances, not use reciprocals.