Question

A battery of internal resistance $r$ having no load resistance has an e.m.f. $E$ volt. What is the observed e.m.f across the terminals of the battery when a load resistance $R(=r)$ is connected to its terminals?

• A. $2Evolt$
• B. $Evolt$
• C. $\frac{E}{2}volt$
• D. $\frac{E}{4}volt$

Answer 1

The correct option is C $\frac{E}{2}volt$

Circuit diagram for the problem can be drawn as shown below.

where $r=$ internal resistance of the battery
$R(=r)=$ load resistance
$V=$ Potential across the terminals of battery
Since the resistors are in series, the equivalent resistance,
$R_{eq}=r+r=2r$
Current through the circuit, $E=I\times R_{eq}=I\times 2r$
$\begin{array}{}\Rightarrow I=\frac{E}{2r}& \text{(1)}\end{array}$
Relation between emf, potential and current can be written as,
$V=E-Ir$
Substituting the value of $I$ from (1),
$V=E-\frac{E}{2r}\times r=\frac{E}{2}V$