In a series circuit, how is the total resistance determined?

• A. Product of the resistances
• B. Harmonic mean of the resistances
• C. Reciprocal of the sum
• D. Sum of the resistances

Answer: (D)

In a series circuit, the same current flows through every component, and the voltages across each resistor add up to the total voltage. Using Ohm’s law, each drop is V_i = I·R_i, so the total voltage is V_total = I(R1 + R2 + …). Since the current is the same through the whole string, the total resistance is defined by V_total = I·R_total, which gives R_total = R1 + R2 + … . That’s why resistances simply add in series.

The other forms don’t describe how series circuits behave. A product would imply a multiplication of oppositions, which isn’t how a single current path accumulates resistance. The reciprocal of a sum isn’t consistent with V = IR for a common current. The harmonic mean is associated with particular averaging or parallel-type relationships, not a series path.