Name: Series and Parallel Connection
Uploaded: 2019-07-19
Duration: 4 min 25 s
Description: How do different arrangements of components in a circuit affect its performance? We first need to learn about the two prominent types of circuit connections....

Question

For three resistors connected in series, prove that the equivalent resistance is equal to the sum of the individual resistances.

Accepted Answer

In the given circuit, the resistances $R_{1}$ , $R_{2}$ and $R_{3}$ are connected in series across a cell of potential difference $V$ as shown in the circuit diagram given below:

When current flows through a resistance, a potential drop occurs across the resistance. This potential difference can be found by Ohm's law.
The potential drop across resistance $R_{1}$ is $V_{1} = I R_{1}$
The potential drop across resistance $R_{2}$ is $V_{2} = I R_{2}$
The potential drop across resistance $R_{3}$ is $V_{3} = I R_{3}$

The potential differences across the three resistors are produced by the source of potential difference $V$ of the circuit, the cell. Therefore,

$V = V_{1} + V_{2} + V_{3} V = I R_{1} + I R_{2} + I R_{3} V = I (R_{1} + R_{2} + R_{3})$

Let $R$ , be the equivalent resistance, then the potential difference across $R_{s}$ is

$V = I R_{s} I R_{s} = I (R_{1} + R_{2} + R_{3}) R_{s} = R_{1} + R_{2} + R_{3}$

Thus, when three resistors are connected in series, their equivalent resistance is the sum of the individual resistances.

For three resistors connected in series, prove that the equivalent resistance is equal to the sum of the individual resistances.

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