For resistors in parallel, 2 Ω and 4 Ω, what is the equivalent resistance?

For resistors in parallel, 2 Ω and 4 Ω, what is the equivalent resistance?

• A. 0.75 Ω
• B. 1 Ω
• C. 0.67 Ω
• D. 1.33 Ω

Answer: (D)

When resistors are in parallel, the total or equivalent resistance is found by adding the reciprocals of each resistance and then taking the reciprocal of that sum. This comes from the fact that the same voltage drives currents through all paths, so the total current is the sum of the individual branch currents, and R_eq = V / I_total simplifies to 1 / (1/R1 + 1/R2 + ...). For 2 Ω and 4 Ω in parallel: 1/R1 + 1/R2 = 1/2 + 1/4 = 0.5 + 0.25 = 0.75 R_eq = 1 / 0.75 = 1.333... Ω, which is 1.33 Ω when rounded. So the equivalent resistance is about 1.33 Ω. This value is indeed less than either individual resistor, reflecting the parallel configuration providing multiple current paths.

When resistors are in parallel, the total or equivalent resistance is found by adding the reciprocals of each resistance and then taking the reciprocal of that sum. This comes from the fact that the same voltage drives currents through all paths, so the total current is the sum of the individual branch currents, and R_eq = V / I_total simplifies to 1 / (1/R1 + 1/R2 + ...).

For 2 Ω and 4 Ω in parallel:

1/R1 + 1/R2 = 1/2 + 1/4 = 0.5 + 0.25 = 0.75

R_eq = 1 / 0.75 = 1.333... Ω, which is 1.33 Ω when rounded.

So the equivalent resistance is about 1.33 Ω. This value is indeed less than either individual resistor, reflecting the parallel configuration providing multiple current paths.