In a series circuit, total resistance equals the sum of the individual resistances. Which statement is true about this property?

In a series circuit, total resistance equals the sum of the individual resistances. Which statement is true about this property?

• A. Total resistance equals the sum of the component resistances
• B. Total resistance is the reciprocal of the sum of reciprocals
• C. Total resistance equals the product of resistances divided by the sum
• D. Total resistance equals the largest resistance

Answer: (A)

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 for each resistor, V1 = I R1, V2 = I R2, and so on, the total voltage is V_total = I(R1 + R2 + ...). Since total resistance is defined by R_total = V_total / I, you get R_total = R1 + R2 + ... Thus the total resistance is the sum of the individual resistances. The other expressions describe different situations: the reciprocal of the sum of reciprocals is for parallel circuits, the product over the sum isn’t the correct relation for series, and the total would only equal the largest resistance in a degenerate case where the others contribute nothing. So the statement that the total resistance equals the sum of the component resistances is the true description for series circuits.

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 for each resistor, V1 = I R1, V2 = I R2, and so on, the total voltage is V_total = I(R1 + R2 + ...). Since total resistance is defined by R_total = V_total / I, you get R_total = R1 + R2 + ... Thus the total resistance is the sum of the individual resistances. The other expressions describe different situations: the reciprocal of the sum of reciprocals is for parallel circuits, the product over the sum isn’t the correct relation for series, and the total would only equal the largest resistance in a degenerate case where the others contribute nothing. So the statement that the total resistance equals the sum of the component resistances is the true description for series circuits.