Ohm's law for a resistor is V = IR. What is the total resistance of two identical resistors in parallel?

Ohm's law for a resistor is V = IR. What is the total resistance of two identical resistors in parallel?

• A. 2R
• B. R
• C. R√2
• D. R/2

Answer: (D)

When resistors are in parallel, the total resistance is smaller because the current has multiple paths to flow through. For two identical resistors each with resistance R, the combined resistance is found from 1/R_eq = 1/R + 1/R = 2/R, so R_eq = R/2. You can also see it with Ohm’s law: the voltage across the parallel network is the same across both resistors, so each carries current I = V/R. The total current is I_total = I + I = 2V/R. Then R_eq = V / I_total = V / (2V/R) = R/2. Intuitively, doubling the current at the same voltage halves the effective resistance. The result would be different if the resistors were in series (giving 2R) or if you misapplied the setup (which wouldn’t yield R). The correct outcome is half the resistance of a single resistor.

When resistors are in parallel, the total resistance is smaller because the current has multiple paths to flow through. For two identical resistors each with resistance R, the combined resistance is found from 1/R_eq = 1/R + 1/R = 2/R, so R_eq = R/2.

You can also see it with Ohm’s law: the voltage across the parallel network is the same across both resistors, so each carries current I = V/R. The total current is I_total = I + I = 2V/R. Then R_eq = V / I_total = V / (2V/R) = R/2. Intuitively, doubling the current at the same voltage halves the effective resistance.

The result would be different if the resistors were in series (giving 2R) or if you misapplied the setup (which wouldn’t yield R). The correct outcome is half the resistance of a single resistor.