Understanding Series Resistance

When resistors are connected in series, the total resistance increases because the current must pass through each resistor sequentially. This calculator helps you compute the total resistance (\(R_{\text{total}} \)) of resistors in series, which is crucial for designing circuits with the desired resistance and voltage drop.

Formula:

The formula for total resistance in a series connection is:

\[R_{\text{total}} = R_1 + R_2 + \dots + R_n\]

Where:

• \( R_{\text{total}} \): Total resistance (in ohms, \( \Omega \))
• \( R_1, R_2, \dots, R_n \): Individual resistor values in the series configuration

Example Calculation:

Let’s compute the total resistance for three resistors connected in series with the following values:

• \( R_1 = 10 \, \Omega \)
• \( R_2 = 20 \, \text{k}\Omega = 20,000 \, \Omega \)
• \( R_3 = 30 \, \text{M}\Omega = 30,000,000 \, \Omega \)

Step-by-Step Solution:

1. Apply the formula:
   \[R_{\text{total}} = R_1 + R_2 + R_3\]
   Substitute the resistor values:
   \[R_{\text{total}} = 10 + 20,000 + 30,000,000\]
2. Sum the resistances:
   \[R_{\text{total}} = 30,020,010 \, \Omega\]

Final Result:

The total resistance of the resistors connected in series is:

\( R_{\text{total}} = 30,020,010 \, \Omega \) or approximately 30 MΩ