In a series circuit, total resistance is obtained by which relationship?

In a series circuit, total resistance is obtained by which relationship?

• A. The total resistance equals the sum of the individual resistances.
• B. Total resistance is the product of the resistances.
• C. Total resistance is the reciprocal of the sum.
• D. Total resistance equals the largest resistance.

Answer: (A)

In a series circuit, the same current flows through every component, so each resistor adds its opposition to that current. Because the current is identical through all elements, the total resistance is simply the sum of the individual resistances: R_total = R1 + R2 + ... . This is why that additive relationship is the correct description for a series connection. For example, 4 ohms and 6 ohms in series give a total of 10 ohms; the current from a given source would be V/10, not V/(4×6) or V divided by the reciprocal sum. The product of resistances or the reciprocal of the sum doesn’t reflect how a series string blocks current, and the largest resistor alone doesn’t determine the total resistance since every resistor contributes to the overall opposition.

In a series circuit, the same current flows through every component, so each resistor adds its opposition to that current. Because the current is identical through all elements, the total resistance is simply the sum of the individual resistances: R_total = R1 + R2 + ... . This is why that additive relationship is the correct description for a series connection.

For example, 4 ohms and 6 ohms in series give a total of 10 ohms; the current from a given source would be V/10, not V/(4×6) or V divided by the reciprocal sum. The product of resistances or the reciprocal of the sum doesn’t reflect how a series string blocks current, and the largest resistor alone doesn’t determine the total resistance since every resistor contributes to the overall opposition.