Question

A cell of e.m.f E and internal resistance r is connected across a resistance r. The potential difference between the terminals of the cell must be

• A. E
• B. E/2
• C. 3E/4
• D. 3E

Answer 1

The correct option is B

E/2

Step 1: Given

Given, a cell EMF E and internal resistance r is connected across a resistance r.

Step 2: Formula Used

By Ohm's law, the voltage is the product of current and resistance $V=ir$. Here, an EMF is produced and the resistances are connected in series, so the formula will be $E=i\left(r+r\right)$. Here, $\mathrm{i}$ is the current through the circuit.

Step 3: Find the current passing through the circuit

$$\begin{gathered} i(r+r)=E \\ i=\frac{E}{(r+r)} \\ i=\frac{E}{2r} \end{gathered}$$

Step 4: Find potential difference across cell

Now, the potential difference(V) between the terminal, $V=E-ir$

put value of $\mathrm{i}$,

$$\begin{gathered} V=E-\left(\frac{E}{2r}\right)r \\ V=E-\frac{E}{2} \\ V=\frac{E}{2} \end{gathered}$$

Thus, the potential difference across the terminals of cell is $\frac{E}{2}$.

Hence, option B is correct.