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Physics Formulas

Resistors in Series Formula

We know that resistors are something that resists the current in a circuit. Furthermore, a resistor in a series is a connected resistor in a line. Furthermore, you will learn about resistors, resistors in a series, resistors in a series formula, its derivation and solved examples. Moreover, after completing the topic you will be able to understand resistors in a series.

resistors in a series formula

Resistors

A resistor refers to an electrical component that regulates and limits the flow of electrical current in an electric circuit. Also, we can use it to provide a specific voltage for an active device such as a transistor. Besides, if all the factors are equal then the direct current (DC) circuit, the current through a resistor is directly proportional to the voltage across the circuit and inversely proportional to its resistance.

Resistors in a Series

It is a series of connected resistors which are daisy-chained together in a single line. Subsequently, all the current flowing through the circuit firstly pass through the first resistor and after that, it will pass through the second resistor because it has no other way to go it must and then third and so on.

Also, the resistor series has a common current flowing through them means that the current that flows through the first resistor must also pass through the second resistor and so on because they are in the path of current.

Most noteworthy, the amount of current that flows through a set of a resistor in a series will be the same in the entire series resistor network.

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Resistors in a Series Formula

It is possible to replace a series of a resistor with an equivalent resistor. Also, the equivalent resistance of the number of resistors in a series is the sum of the individual resistance values. Besides, the unit of resistance is Ohm (\(\Omega\)) that is equal to a volt per Ampere (1 \(\Omega\) = 1 V/A). Moreover, over larger resistors with kilo-Ohm (1 \(K\Omega = 10^{3} \Omega\)) or mega-Ohm (1 \(M \Omega = 10^{6} \Omega\)) resistances are common as well.

Equivalent resistance = resistor 1+ resistor 2 + resistor 3 + …..

\(R_{eq}\) = \(R_{1} + R_{2} + R_{3} + \cdot \cdot \cdot \cdot\)

Derivation of the Formula

\(R_{eq}\) = refers to the equivalent resistance in Ohm or larger unit (\(\Omega\) )

\(R_{1}\) = refers to the resistance of first resistor in ohm (\(\Omega\) )
\(R_{2}\) = refers to the resistance of second resistor in ohm (\(\Omega\) )
\(R_{3}\) = refers to the resistance of third resistor in ohm (\(\Omega\) )

Solved Example

Example 1

Find the equivalent resistance of a 480.0 \(K \Omega\), a 320.0 \(K \Omega\), and a 100.0 \(K \Omega\) resistor connected in series?

Solution:

\(R_{eq}\) = \(R_{1} + R_{2} + R_{3} + \cdot \cdot \cdot \cdot\)

∴ \(R_{eq}\) = \(R_{1} + R_{2} + R_{3}\)

\(R_{eq}\) = 480.0 \(K \Omega\) + 320.0 \(K \Omega\) + 100.0 \(K \Omega\)

\(R_{eq}\) = 900.0 \(K \Omega\)

So, the equivalent resistance of the 480.0 \(K \Omega\), 320.0 \(K \Omega\), 100.0 \(K \Omega\) resistors in the series is 900.0 \(K \Omega\).

Example 2

Two resistors of 240.0 \(K \Omega\), and 8.00 \(M \Omega\) are connected in a series in an electric circuit? Calculate the equivalent resistance?

Solution:

First we need to convert these in common units. Also, in this we need to convert it into mega-Ohms \(M \Omega\).

\(R_{1}\) = 240.0 \(K \Omega\)

\(R_{1}\) = (240.0 \(K \Omega) \left ( \frac{10^{3}\Omega}{1 K \Omega} \right )\left ( \frac{1 M \Omega}{10^{6} \Omega} \right )\)

\(R_{1}\) = (240.0) \(\left ( \frac{10^{3}}{10^{6}} \right ) M \Omega\)

\(R_{1}\) = (240.0) (\(10^{+3-6}) M \Omega\)

\(R_{1}\) = (240.0) (\(10^{-3}) M \Omega\)

\(R_{1}\) = 0.2400 \(M \Omega\)

Now put the values in equivalent resistance formula

\(R_{eq}\) = \(R_{1} + R_{2} + R_{3} + \cdot \cdot \cdot \cdot\)

∴ \(R_{eq}\) = \(R_{1} + R_{2}\)

\(R_{eq}\) = \( 0.2400 m \Omega + 8.00 M \Omega\)

\(R_{eq}\) = \( 8.24 M \Omega\)

So, the equivalent resistance of 240.0 \(K \Omega\), and 8.00 \(M \Omega\) resistors in a series is \( 8.24 M \Omega\).

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