In a series circuit, the total resistance is equal to

In a series circuit, the total resistance is equal to

• A. R = R1 + R2 + R3
• B. R = 1/(1/R1 + 1/R2 + 1/R3)
• C. R = R1 - R2 - R3
• D. R = R1 * R2 * R3

Answer: (A)

In a series circuit, the same current flows through every component, so each resistor adds to the total opposition the current faces. The total resistance is simply the sum of all resistances: R_total = R1 + R2 + R3. This follows from V = IR: the total voltage equals I times the total resistance, and since the voltages across each resistor add up (Vi = I Ri), you get V_total = I(R1 + R2 + R3). The other forms correspond to different arrangements or operations: 1/(1/R1 + 1/R2 + 1/R3) is for parallel circuits; subtraction or multiplication of resistances doesn’t reflect how series resistors combine. For example, with R1 = 2 Ω, R2 = 3 Ω, and R3 = 5 Ω, the total in series is 10 Ω, larger than any individual resistor.

In a series circuit, the same current flows through every component, so each resistor adds to the total opposition the current faces. The total resistance is simply the sum of all resistances: R_total = R1 + R2 + R3. This follows from V = IR: the total voltage equals I times the total resistance, and since the voltages across each resistor add up (Vi = I Ri), you get V_total = I(R1 + R2 + R3). The other forms correspond to different arrangements or operations: 1/(1/R1 + 1/R2 + 1/R3) is for parallel circuits; subtraction or multiplication of resistances doesn’t reflect how series resistors combine. For example, with R1 = 2 Ω, R2 = 3 Ω, and R3 = 5 Ω, the total in series is 10 Ω, larger than any individual resistor.