Question

The internal resistance of a \[2.1V\] cell which gives a current of $0.2A$ through a resistance of $10\Omega $ is:
A) $0.2\Omega $
B) $0.5\Omega $
C) $0.8\Omega $
D) $1.0\Omega $

Answer 1

Hint: We know that internal and external resistance are the two different aspects. So, we will denote these two properties with two different variables. Now, in the question we are given external resistance, current and voltage of the cell. Now, we know that there is a relation between all these quantities which is given by ohm’s law. Hence, we will use ohm’s law to calculate the internal resistance of the cell by substituting the values.

Formula used:
We will use ohm’s law, that is \[V = I\left( {R + r} \right)\]
Where, $V$ is voltage, $I$ is current, $R$ is external resistance and $r$ is internal resistance.

Complete step by step solution:
In the above question, we can see that
Internal resistance is \[2.1V\], current is $0.2A$ , external resistance is $10\Omega $.
Now, to calculate internal resistance, we will use ohm’s law.
Now, we know that ohm’s law is \[V = I\left( {R + r} \right)\], where, $V$ is voltage, $I$ is current, $R$ is external resistance and $r$ is internal resistance.
So, by substituting the values of external resistance, voltage and current in the given equation,
\[
  V = I\left( {R + r} \right) \\
   \Rightarrow 2.1 = \left( {0.2} \right)\left( {10 + r} \right) \\
   \Rightarrow 10 + r = \dfrac{{21}}{2} \\
   \Rightarrow r = \dfrac{{21}}{2} - 10 \\
 \]
Now, by simplifying the above value,
We get,
$r = 0.5\Omega $
Hence, the internal resistance of the given cell is $0.5\Omega $ .

Hence, the correct option is (B).

Note: In the above problem we have to note that internal and external resistance are different properties and we know that total resistance is the sum of internal and external resistance. Now, in the calculation part we have to take two variables for internal and external resistance. Now, by substituting the values and simplifying the equation, we will get our answer.