Question

A car bulb connected to a \[12\,{\text{volt}}\] battery draw \[{\text{2}}\,{\text{A}}\] current while glowing. What is the resistance of the filament of the bulb?
A.\[3\,\Omega \]
B.\[6\,\Omega \]
C.\[9\,\Omega \]
D.\[24\,\Omega \]

Answer 1

Hint:Use ohm’s law to determine the resistance of the filament of the bulb. This law gives the relation between the voltage, current and resistance of a current carrying conductor.

Formula used:
The expression for Ohm’s law is
\[I = \dfrac{V}{R}\]
Here, \[I\] is the current through the conductor, \[V\] is the potential difference across the two ends of the conductor and \[R\] is the resistance of the conductor.

Complete step by step answer:
According to Ohm’s law, the current \[I\] through any two points of the conductor is directly proportional to the potential difference \[V\] across those points of the conductor.
\[I \propto V\]
\[ \Rightarrow I = \dfrac{V}{R}\] …… (1)
Here, the resistance \[R\] of the conductor is the constant of proportionality.
The car bulb is connected to a battery of potential difference (voltage) \[12\,{\text{volt}}\] and current \[{\text{2}}\,{\text{A}}\].
Calculate the resistance of the filament of the bulb.
Rearrange equation (1) for Ohm’s law for resistance \[R\] of filament of the bulb.
\[ \Rightarrow R = \dfrac{V}{I}\]
Substitute \[12\,{\text{V}}\] for \[V\] and \[{\text{2}}\,{\text{A}}\] for \[I\] in the above equation.
\[ \Rightarrow R = \dfrac{{12\,{\text{V}}}}{{2\,A}}\]
\[ \Rightarrow R = 6\,\Omega \]
Therefore, the resistance of the filament of the bulb is \[6\,\Omega \].
Hence, the correct option is B.
Additional information:
The conductors which obey the Ohm’s law are known as the Ohmic conductor. The semi-conductors obey Ohm’s law only for low electric fields. For high electric fields, Ohm’s law is not obeyed because the current becomes independent of the applied field.

Note: While using Ohm’s law to determine the resistance, current or voltage, make sure that the conductor through which the current is flowing is Ohmic conductor and physical quantity such as temperature should be constant.