Question

A cell of e.m.f. $E$ having an internal resistance $r$ is connected to an external resistance $R$. The potential difference $V$ across the resistance $r$ varies with $R$ as shown in the figure by the curves

• A. $A$
• B. $B$
• C. $C$
• D. $D$

Answer 1

The correct option is D $D$

$\text{Step 1: Current in circuit[Refer Figure]}$

Applying KVL, for simple circuit with a battery and few resistances in a single loop, Current is given by $I=\frac{E}{R_{eq}}$

$\Rightarrow I=\frac{E}{r+R}$

$\text{Step 2: Voltage across Internal Resistance r}$

The voltage across internal resistance $r$ would be $V$ that is

$V=I\times r$

$\Rightarrow V=\frac{Er}{r+R}$

Therefore, At $R=0,V=E$

And, As the value of $R$ increases, the value of $V$ will decrease.

Hence, the correct option is D