What is the equivalent resistance of two resistors in series?

What is the equivalent resistance of two resistors in series?

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

Answer: (D)

In a series connection, the same current flows through both resistors and the voltages add. The total voltage across the two is V_total = V1 + V2, and since V = I·R for each resistor, V_total = I(R1 + R2). The equivalent resistance is defined as V_total divided by the current I, so R_eq = (R1 + R2). This shows why you simply add the resistances for a series path—the current is the same through each element, and the total resistance is the sum of the individual resistances. For example, if R1 is 4 ohms and R2 is 6 ohms, the equivalent resistance is 10 ohms. The other formulas correspond to parallel connections, where the total resistance is less than either resistor.

In a series connection, the same current flows through both resistors and the voltages add. The total voltage across the two is V_total = V1 + V2, and since V = I·R for each resistor, V_total = I(R1 + R2). The equivalent resistance is defined as V_total divided by the current I, so R_eq = (R1 + R2). This shows why you simply add the resistances for a series path—the current is the same through each element, and the total resistance is the sum of the individual resistances. For example, if R1 is 4 ohms and R2 is 6 ohms, the equivalent resistance is 10 ohms. The other formulas correspond to parallel connections, where the total resistance is less than either resistor.