Question

A car bulb connected to a $12V$ battery draws $2A$ current when glowing. What is the resistance of the filament of the bulb? Will the resistance be more, same or less when the bulb is not glowing?

Answer 1

Hint : In order to solve this question, we will understand resistance of any filament is property of filament to offer opposition to the motion of current through filament. Mathematically Resistance is defined as voltage per current. Its SI Unit is Ohm denoted as $\Omega$ . Also a wire having $0\Omega$ offers little or no resistance to motion of current whereas wire having $\infty$ resistance offers highest resistance.

Complete Step By Step Answer:
As given in problem, Voltage difference across filament $V = 12$ volts
Current flows through filament $I = 2$ Ampere
So from definition, Resistance is defined as $R = \dfrac{V}{I}$
Putting values in formula we get $R = \dfrac{{12}}{2}$ $\Omega$
Or $R = 6$ $\Omega$
So the answer to first part is Resistance of filament is $6$ $\Omega$
If the bulb is not glowing there could be possibility that either filament is not connected to voltage difference or due to some internal problems no current flows in filament although it connects to voltage difference.
Let us explore both possibilities
Possibility first that is not connected to voltage difference i.e. $V = 0$ volt
So putting value in resistance formula we get $R = \dfrac{0}{I}$ $\Omega$ or $R = 0$ $\Omega$
So in this case resistance is less
Possibility second when no current flows through it i.e. $I = 0$ ampere
So putting in resistance formula we get $R = \dfrac{V}{0}$ or $R = \infty$
So in this case resistance is large.

Note :
It should be remembered that resistance is an inherent property of material and it is in line with Newton’s first law of motion in which inertia states that the body opposes any change in its state. So similarly resistance is the effect that the body shows whenever current flows and its state changes. The body which offers low resistance is known as conductor and body which offers high resistance is an insulator.