One method for finding the total resistance of parallel resistors is to multiply the resistances and divide by their sum.

One method for finding the total resistance of parallel resistors is to multiply the resistances and divide by their sum.

• A. Not applicable
• B. Only for parallel
• C. False
• D. True

Answer: (D)

For two resistors in parallel, the total resistance is found by multiplying the resistances and dividing by their sum. This works because in parallel the voltage across each resistor is the same and currents add: I1 = V/R1 and I2 = V/R2, so I_total = V/R1 + V/R2 = V(1/R1 + 1/R2). The equivalent resistance is R_eq = V / I_total = V / [V(1/R1 + 1/R2)] = 1/(1/R1 + 1/R2) = (R1*R2)/(R1+R2). So the product over the sum is the correct shortcut for two parallel resistors. For more than two resistors, use 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ..., or reduce step by step with the same idea.

For two resistors in parallel, the total resistance is found by multiplying the resistances and dividing by their sum. This works because in parallel the voltage across each resistor is the same and currents add: I1 = V/R1 and I2 = V/R2, so I_total = V/R1 + V/R2 = V(1/R1 + 1/R2). The equivalent resistance is R_eq = V / I_total = V / [V(1/R1 + 1/R2)] = 1/(1/R1 + 1/R2) = (R1*R2)/(R1+R2). So the product over the sum is the correct shortcut for two parallel resistors. For more than two resistors, use 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ..., or reduce step by step with the same idea.