What is the formula for the equivalent resistance of resistors in series?

What is the formula for the equivalent resistance of resistors in series?

• A. R_eq = R1 R2 / (R1 + R2)
• B. R_eq = 1 / (1/R1 + 1/R2)
• C. R_eq = R1 + R2
• D. R_eq = (R1 + R2)/2

Answer: (C)

When resistors are arranged in series, the same current flows through each one, and the voltages across them add up. The total voltage across both is V_total = V1 + V2, and with V = I R for each resistor, V_total = I R1 + I R2 = I (R1 + R2). The equivalent resistance is defined by V_total = I × R_eq, so R_eq = R1 + R2. The other forms shown correspond to resistors in parallel (R_eq = (R1 R2)/(R1 + R2) or 1/(1/R1 + 1/R2)) or an incorrect averaging (R1 + R2)/2, which does not describe series behavior.

When resistors are arranged in series, the same current flows through each one, and the voltages across them add up. The total voltage across both is V_total = V1 + V2, and with V = I R for each resistor, V_total = I R1 + I R2 = I (R1 + R2). The equivalent resistance is defined by V_total = I × R_eq, so R_eq = R1 + R2.

The other forms shown correspond to resistors in parallel (R_eq = (R1 R2)/(R1 + R2) or 1/(1/R1 + 1/R2)) or an incorrect averaging (R1 + R2)/2, which does not describe series behavior.