Question

A battery of internal resistance $r$ having no load reistance has an emf $E\text{Volt}$. What will be the potential across the terminals of the battery when a load reistance $R(=r)$ is connected to its terminals?

• A. $2E\text{Volt}$
• B. $E\text{Volt}$
• C. $E/2\text{Volt}$
• D. $E/4\text{Volt}$

Answer 1

The correct option is C $E/2\text{Volt}$

With load resistance, circuit can be drawn as:


Current in the circuit, $i=\frac{E}{R+r}=\frac{E}{2r}$

Potential across terminals, $V=E-ir$

$\Rightarrow V=E-\frac{E}{2r}r\Rightarrow V=\frac{E}{2}$

Why this question? Generally, we come across two possible battery cases: Case I: Battery acting as a source (or battery is discharging) Terminal voltage, $V_A-V_B=\epsilon -ir$ Case II: Battery acting as a load (or battery charging) $V_A-V_B=\epsilon +ir$