Comparing Resistances in Parallel

📌 CONCEPT: When resistors are connected in parallel, the total resistance of the circuit is less than the resistance of a single resistor.

📐 RULE / FORMULA: The reciprocal of the total resistance (Rt) is equal to the sum of the reciprocals of the individual resistances (R1, R2, R3) in a parallel circuit, given by the formula: 1/Rt = 1/R1 + 1/R2 + 1/R3.

💡 WORKED EXAMPLE: Consider three identical resistors (R1 = R2 = R3 = 2 ohms) connected in parallel. Using the formula, we find 1/Rt = 1/2 + 1/2 + 1/2 = 3/2. Therefore, Rt = 2/3 ohms. Since 2/3 ohm is less than 2 ohms, the total resistance of the circuit is less than the resistance of a single resistor.

⚠️ COMMON MISTAKE: Students often mistakenly think that the total resistance of a parallel circuit is equal to the resistance of a single resistor, failing to account for the increased current flow and reduced total resistance.