Resistors in Parallel: A Conundrum

📌 CONCEPT: When resistors are connected in parallel, the equivalent resistance (R_eq) is less than the individual resistance (R) of each resistor, and the total current (I) is the sum of the currents through each resistor.

📐 RULE / FORMULA: The formula for equivalent resistance in parallel is 1/R_eq = 1/R_1 + 1/R_2 +... + 1/R_n, and the total current is I = I_1 + I_2 +... + I_n.

💡 WORKED EXAMPLE: Suppose two of the 10-ohm light bulbs are removed, leaving only one 10-ohm bulb. The equivalent resistance of the remaining configuration is R_eq = 10 ohms, and the total current is I = V/R_eq = 100/10 = 10 A. The current through the remaining bulb is I = V/R = 100/10 = 10 A.

⚠️ COMMON MISTAKE: Students often confuse the equivalent resistance in parallel with the individual resistance, and forget to use the correct formula for equivalent resistance.