Question

a small bulb has a resistance of 2 ohm when cold it take up a current of 0.4 ampere from a source of 4v then start glowing? calculate resistance when it is glow and elaborate the reason of difference between resistance ?

Answer 1

The resistance of the bulb in glow condition is $\boxed{10\,\Omega}$.

Further explanation:

The resistance of a conductor changes with change in the temperature of the conductor. When temperature of a conductor increased the energy of atoms inside the conductor also increase, which causes molecules and atoms of conductor to collide on each other. This random collision of atoms will restrict the flow of electrons, therefore resistance will increase.

Given:

The resistance of a small bulb is $2\text{ ohm}$ when cold.

Current in the circuit is $0.4\text{ A}$.

Source has an EMF of $4.0\text{ V}$.

Concept:

Bulb take up a current of $0.4\text{ A}$ from a source of $4\text{ V}$ and starts glowing. As the bulb glows the temperature of the filament increase and the resistance of the filament also increase.

Let $R$ is the resistance of the bulb when it is glow.

The equivalent circuit for the filament of bulb is shown in the figure attached below.

Use the relation of Ohm's law to calculate the resistance of the bulb.

$R=\dfrac{V}{I}$

Substitute the values of $V$ and $I$ in above expression.

$\begin{aligned}R&=\dfrac{4}{0.4}\\&=10\,\Omega\end{aligned}$

Thus, the resistance of the bulb in glow condition is $\boxed{10\,\Omega}$.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Electricity

Keywords:

Bulb, resistance, 2 ohm, cold, 0.4 A, 0.4 ampere, 4 V, glowing, KVL, temperature, ohms law, conductor, collision, kinetic theory, gas, EMF, molecules, atoms, electrons, random motion.

Answer 2

The resistance of the bulb when it is cold is $R=2 \Omega$.

The resistance of the bulb when it is crossed by a current of I=0.4 A under a potential difference of $V=4.0 V$ can be calculated by using Ohm's law:
$R= \frac{V}{I}= \frac{4 V}{0.4 A}=10 \Omega$

The reason for this difference in the resistance is the following: when the current passes through the bulb, the bulb heats up, and an increase in temperature in the filament of the bulb causes an increase in resistance of the filament. In fact, the resistance of a resistor increases as the temperature increases, because the atoms of the lattice of the material vibrate more (due to their greater energy) and therefore the electrons of the current are more likely to collide with them. As a result, the resistance of the material increases.