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: Understanding the Question:
The question asks for the correct rule governing the equivalent or total resistance when multiple resistors are connected end-to-end in a series configuration.

Step 2: Key Formula or Approach:
For a series connection of \(n\) resistors with resistances \(R_1, R_2, \dots, R_n\), the equivalent resistance \(R_{eq}\) is given by:
\[ R_{eq} = R_1 + R_2 + \dots + R_n \]

Step 3: Detailed Explanation:

• In a series circuit, there is only one path for the electric current to flow. Therefore, the same current (\(I\)) flows through each resistor.

• The total potential difference (\(V\)) across the entire combination is equal to the sum of the individual potential drops across each resistor:
\[ V = V_1 + V_2 + \dots + V_n \]

• Applying Ohm's law (\(V = I R\)) to each component:
\[ I R_{eq} = I R_1 + I R_2 + \dots + I R_n \]

• Dividing the entire equation by the common current \(I\), we get:
\[ R_{eq} = R_1 + R_2 + \dots + R_n \]

• This confirms that the total resistance is indeed the direct algebraic sum of the individual resistances, which makes the total resistance greater than any individual resistance in the circuit.


Step 4: Final Answer:
Hence, the correct statement is that the total resistance is the sum of all the individual resistances.