Question

Two resistors of resistance $2R$ and $3R$ are connected in series with a battery, which has an emf of $E$ and an internal resistance $R$. What is the potential difference across the resistor of resistance $2R$?

Answer 1

Series connection

1. When the components of the circuit are connected end to end, the connection is called a series connection.
2. In a series connection, the same current flows through the circuit.

Step 1: Equivalent resistance

The equivalent resistance of the circuit can be calculated by adding the individual resistances.

$$\begin{gathered} R_{eq}=2R+3R+R \\ {R}_{eq}=6R \end{gathered}$$

Here, $R_{eq}$ is the equivalent resistance.

Step 2: Calculation of the total current in the circuit

$$\begin{gathered} i=\frac{E}{R_{eq}} \\ i=\frac{E}{6R} \end{gathered}$$

Here, $i$ is the total current in the circuit and $E$ is the emf.

Step 3: Calculation of potential difference across the resistor of resistance $2R$

$p=i\times 2R$

Here, $p$ is the potential difference.

$$\begin{gathered} p=\frac{E}{6R}\times 2R \\ p=\frac{E}{3} \end{gathered}$$

Hence, the potential difference across the resistor of resistance $2R$ is $\frac{E}{3}$.