What is the expression for equivalent resistance if resistors are connected in series?
2 Answers
When resistors are connected in series, the total or equivalent resistance is simply the sum of the individual resistances. This is because, in a series circuit, the current flowing through each resistor is the same, and the total voltage drop across the series combination is the sum of the voltage drops across each resistor.
Here's the general formula for calculating the equivalent resistance (\( R_{\text{eq}} \)) of resistors connected in series:
\[ R_{\text{eq}} = R_1 + R_2 + R_3 + \cdots + R_n \]
where \( R_1, R_2, R_3, \ldots, R_n \) are the resistances of the individual resistors connected in series.
### Example:
If you have three resistors connected in series with resistances \( 4 \, \Omega \), \( 5 \, \Omega \), and \( 6 \, \Omega \), the equivalent resistance is calculated as:
\[ R_{\text{eq}} = 4 \, \Omega + 5 \, \Omega + 6 \, \Omega = 15 \, \Omega \]
So, the total or equivalent resistance of these three resistors in series is \( 15 \, \Omega \).
Here's the general formula for calculating the equivalent resistance (\( R_{\text{eq}} \)) of resistors connected in series:
\[ R_{\text{eq}} = R_1 + R_2 + R_3 + \cdots + R_n \]
where \( R_1, R_2, R_3, \ldots, R_n \) are the resistances of the individual resistors connected in series.
### Example:
If you have three resistors connected in series with resistances \( 4 \, \Omega \), \( 5 \, \Omega \), and \( 6 \, \Omega \), the equivalent resistance is calculated as:
\[ R_{\text{eq}} = 4 \, \Omega + 5 \, \Omega + 6 \, \Omega = 15 \, \Omega \]
So, the total or equivalent resistance of these three resistors in series is \( 15 \, \Omega \).
When resistors are connected in series, the total or equivalent resistance is simply the sum of the individual resistances. The expression for the equivalent resistance \( R_{eq} \) in a series circuit is:
\[ R_{eq} = R_1 + R_2 + R_3 + \cdots + R_n \]
where \( R_1, R_2, R_3, \ldots, R_n \) are the resistances of the individual resistors connected in series.
This is because in a series connection, the current flowing through each resistor is the same, and the total voltage drop across the series of resistors is the sum of the voltage drops across each resistor. Thus, the equivalent resistance is the sum of the individual resistances.
\[ R_{eq} = R_1 + R_2 + R_3 + \cdots + R_n \]
where \( R_1, R_2, R_3, \ldots, R_n \) are the resistances of the individual resistors connected in series.
This is because in a series connection, the current flowing through each resistor is the same, and the total voltage drop across the series of resistors is the sum of the voltage drops across each resistor. Thus, the equivalent resistance is the sum of the individual resistances.