In a series circuit, how is the total resistance related to the individual resistances?

• A. R_total = R1 × R2 + ...
• B. R_total = R1 + R2 + ...
• C. R_total = 1 / (1/R1 + 1/R2)
• D. R_total = R1 − R2

Answer: (B)

In a series circuit, the same current flows through every component, so the voltage drops across each resistor add up. Using Ohm’s Law, each drop is V_i = I R_i, and the total voltage is V_total = V1 + V2 + ... = I(R1 + R2 + ...). Since V_total also equals I R_total, it follows that R_total = V_total / I = R1 + R2 + ... . So the resistances simply add in series because the current is the same through all of them and the total voltage is the sum of the individual drops. The other forms would not reflect this straightforward additive behavior in series, whereas parallel circuits combine resistances with a reciprocal sum because the voltage is the same across each branch and currents split.