What is the total resistance of three 12-ohm resistors connected in parallel?

What is the total resistance of three 12-ohm resistors connected in parallel?

• A. 2 Ohms
• B. 12 Ohms
• C. 4 Ohms
• D. 36 Ohms

Answer: (C)

Resistors in parallel provide multiple paths for current, so the overall resistance is smaller than any single resistor. For parallel connections, the reciprocals add: 1/R_total = 1/R1 + 1/R2 + 1/R3. With three 12-ohm resistors, 1/R_total = 1/12 + 1/12 + 1/12 = 3/12 = 1/4, so R_total = 4 ohms. A handy shortcut for identical values is R_total = R / n, giving 12 ohms divided by 3 equals 4 ohms. The other options correspond to different setups: 12 ohms would be if only one resistor were involved, 36 ohms would be all in series, and 2 ohms would require six 12-ohm resistors in parallel.

Resistors in parallel provide multiple paths for current, so the overall resistance is smaller than any single resistor. For parallel connections, the reciprocals add: 1/R_total = 1/R1 + 1/R2 + 1/R3. With three 12-ohm resistors, 1/R_total = 1/12 + 1/12 + 1/12 = 3/12 = 1/4, so R_total = 4 ohms. A handy shortcut for identical values is R_total = R / n, giving 12 ohms divided by 3 equals 4 ohms. The other options correspond to different setups: 12 ohms would be if only one resistor were involved, 36 ohms would be all in series, and 2 ohms would require six 12-ohm resistors in parallel.