Resistance in a Parallel Circuit?

📌 CONCEPT: In a parallel circuit, the equivalent resistance (R_eq) is less than the individual resistances, and the total current is the sum of the currents through each branch.

📐 RULE / FORMULA: The formula for calculating the equivalent resistance in a parallel circuit is given by 1/R_eq = 1/R1 + 1/R2, where R1 and R2 are the individual resistances.

💡 WORKED EXAMPLE: Given two resistors, R1 = 10 Ω and R2 = 20 Ω, in parallel with 20 V applied across each, we can find their equivalent resistance using the formula: 1/R_eq = 1/10 Ω + 1/20 Ω. Simplifying, we get 1/R_eq = 0.2 Ω^-1 + 0.05 Ω^-1 = 0.25 Ω^-1, so R_eq = 4 Ω. The current through each resistor is given by I = V/R, so I1 = 20 V / 10 Ω = 2 A and I2 = 20 V / 20 Ω = 1 A. Since R_eq is less than the individual resistances, the total current is I_total = I1 + I2 = 3 A, which is more than the current through each resistor.

⚠️ COMMON MISTAKE: Students often confuse the formula for equivalent resistance in series and parallel circuits, which is R_eq = R1 + R2 for series circuits and 1/R_eq = 1/R1 + 1/R2 for parallel circuits.