Rankers Physics

Combination of Batteries: Practice Problem & Solution

The internal resistance of a $2.1 \text{ V}$ cell which gives a current of $0.2 \text{ A}$ through a resistance of $10 \Omega$ is: (2013)
$1.0 \Omega$
$0.2 \Omega$
$0.5 \Omega$
$0.8 \Omega$

Solution Explained:

To solve this problem, we apply the core principles of Combination of Batteries. Understanding the underlying formula is key to arriving at the correct answer below:

Using the relation $I = \frac{E}{R + r}$, we substitute the given values: $0.2 = \frac{2.1}{10 + r}$. Solving for $r$, we get $10 + r = \frac{2.1}{0.2} = 10.5$, which yields $r = 0.5 \Omega$.

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