If two resistors in parallel have equal resistance, how does the total resistance compare to each individual resistor?

• A. R_total is half of each resistance (R/2).
• B. R_total equals the same as each resistance
• C. R_total is double each resistance
• D. R_total is the sum of the two resistances

Answer: (A)

When resistors are connected in parallel, the total resistance becomes smaller because the current has more paths to take. The way to find it is to add the conductances: 1/R_total = 1/R1 + 1/R2. If both resistors have the same value R, then 1/R_total = 1/R + 1/R = 2/R, which gives R_total = R/2. So the total resistance is half of the resistance of one resistor.

Intuitively, each resistor would carry current I = V/R; together they carry 2I at the same voltage, which is equivalent to a single resistor with resistance V/(2I) = R/2. The other possibilities would imply no change, an increase, or a simple sum, none of which matches how parallel paths reduce total resistance.