Question

A battery of e.m.f. $E$ has an internal resistance '$r$'. A variable resistance $R$ is connected to the terminals of the battery. A current $I$ is drawn from the battery. $V$ is the terminal P.D. lf $R$ alone is gradually reduced to zero, which of the following best describes $I$ and $V$?

• A. $I$ approaches $E/r$, $V$ approaches $E$
  
• B. $I$ approaches infinity, $V$ approaches $E$
  
• C. $I$ approaches zero, $V$approaches $E$
  
• D. $I$ approaches $E/r$, $V$ approaches zero

Answer 1

Answer: (D)

$I$ approaches $E/r$, $V$ approaches zero

$\text{Step 1: Finding Current}$

From Figure, Total resistance of the circuit $R_{eq}=R+r$

So, Current in the circuit $I=\frac{E}{R_{eq}}=\frac{E}{R+r}$ $....\left(1\right)$

As $R\to 0$, we get $I\to \frac{E}{r}$

$\text{Step 2: Terminal Potential Difference(V) across the battery}$

From Figure:

$V=V_{AB}=V_{CD}=$ $IR$

$\Rightarrow V=\frac{ER}{R+r}$ $($ Using Equation $\left(1\right))$

From above Equation, As $R\to 0$, we get $V\to 0$.

Thus option $D$ is correct.