Question

When a 4 V battery is connected across an unknown resistor there is a current of 100 mA in the circuit. The value of the resistance of the resistor is:
\[\begin{align}
  & i)\,4\Omega \\
 & ii)\,40\Omega \\
 & iii)\,400\Omega \\
 & iv)\,0.4\Omega \\
\end{align}\]

Answer 1

Hint: The equation that relates the voltage, current and resistance that is, Ohm’s law should be used to solve this problem. As, the values of the voltage and current are given, so, we will be using the same to find the unknown resistance.

Formula used:
\[V=IR\]

Complete step by step solution:
From the given information, we have the data as follows.
The emf of the battery connected in a circuit, \[V=4\,V\]
The current flowing through the circuit, \[I=100\,mA\]
The equation that we are using to solve this problem is,
\[V=IR\]
Where \[I\] is the current, \[V\] is the voltage (emf) and \[R\] is the resistance.

This equation represents Ohm’s law, that is, this relates the voltage, current and resistance of a circuit.
Now, substitute the given values in the above equation.
\[\begin{align}
  & 4=100\,\times {{10}^{-3}}\times R \\
 & \Rightarrow R=\dfrac{4}{100\,\times {{10}^{-3}}} \\
\end{align}\]
Therefore, the value of the resistance of the resistor connected in the circuit is, \[40\Omega \].
\[\therefore \]The value of the resistance of the resistor is \[40\Omega \], thus, the option (ii) is correct.

Additional information:
According to Ohm’s law, the current flowing through the circuit is directly proportional to the emf or the potential difference across the circuit. This proportionality constant is removed by the resistance offered to the flow of current. Other than Ohm’s law, there is no other equation that defines the relationship between the current, voltage and the resistance of a circuit.

Note: The units of the parameters should be taken care of. As, in this case, the units of the voltage and the current are in the SI unit, so, no need to change. This question was based on the concept of Ohm’s law, as it relates to the parameters of the circuit, such as resistance, voltage and current.