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

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

• A. RT equals the product of individual resistances.
• B. RT equals the sum of individual resistances.
• C. RT equals the reciprocal of the sum of reciprocals.
• D. RT equals the average of the individual resistances.

Answer: (B)

In a series circuit, the same current flows through every component, so the total resistance is the sum of all the individual resistances. This comes from Ohm’s law: V_total = I × RT, and each component drops a voltage V_i = I × R_i. The total voltage is the sum of those drops: V_total = V1 + V2 + … = I × (R1 + R2 + …). Since V_total also equals I × RT, it follows that RT = R1 + R2 + …. For example, if you have resistors of 4 Ω and 7 Ω in series, the total resistance is 11 Ω. If the supply is 22 V, the current is I = 22 V / 11 Ω = 2 A, and the voltage drops are V1 = 8 V and V2 = 14 V, adding up to the total 22 V. The other formulas apply to different configurations (for example, parallel circuits use the reciprocal sum of reciprocals), but in a series circuit you simply add the resistances.

In a series circuit, the same current flows through every component, so the total resistance is the sum of all the individual resistances. This comes from Ohm’s law: V_total = I × RT, and each component drops a voltage V_i = I × R_i. The total voltage is the sum of those drops: V_total = V1 + V2 + … = I × (R1 + R2 + …). Since V_total also equals I × RT, it follows that RT = R1 + R2 + ….

For example, if you have resistors of 4 Ω and 7 Ω in series, the total resistance is 11 Ω. If the supply is 22 V, the current is I = 22 V / 11 Ω = 2 A, and the voltage drops are V1 = 8 V and V2 = 14 V, adding up to the total 22 V.

The other formulas apply to different configurations (for example, parallel circuits use the reciprocal sum of reciprocals), but in a series circuit you simply add the resistances.