Question

Which of the following is true when resistors are connected in series?

• A. The total resistance is the product of the individual resistances.
• B. The total resistance is less than any individual resistance.
• C. The total resistance is the sum of all the individual resistances.
• D. The total resistance is equal to the average of the individual resistances.

Hint:

In a series combination, the equivalent resistance is always greater than the largest individual resistance in the circuit.
Remember that current remains constant in a series circuit.

Answer 1

The Correct Option is C

Step 1: Picture a series circuit.
In series, resistors are joined one after another in a single loop, so the same current \(I\) has to pass through every resistor in turn.
Step 2: Add up the voltage drops.
Each resistor causes its own voltage drop, \(V_1 = IR_1\), \(V_2 = IR_2\), and so on, and the battery voltage equals the sum of these drops, \[ V = V_1 + V_2 + \dots + V_n \]
Step 3: Replace with a single equivalent resistor.
If one resistor \(R_{eq}\) is to carry the same current \(I\) and produce the same total drop \(V\), then \(V = I R_{eq}\). Comparing both expressions for \(V\) gives plain addition of resistances.
\[ \boxed{R_{eq} = R_1 + R_2 + \dots + R_n} \]