Question

A small bulb has a resistance of $2\Omega $ when it is cold. It draws $0.4A$ current from a source of $4V$ and then starts glowing. Calculate the resistance when it is glowing.

Answer 1

Hint: In order to solve this question we will use Ohm’s law and formula which gives the relation between current, voltage, and resistance in an electrical circuit. The resistance is directly proportional to temperature. With the rise in temperature, the vibrational movement of the atoms of the conductor increases. Due to an increment in vibration, the probability of collision among atoms and electrons rises. As a result, the resistance of the conductor increases.

Formula used:
\[V = I \times R\]
Where,
$V$ is the voltage,
$I$ is the current and
$R$ is the resistance.

Complete step by step solution:
Here it is given that,
Resistance of the bulb when it is cold, ${R_{cold}} = 2\Omega $ ,
Current, $I = 0.4A$ and
Voltage, $V = 4V$ .
Now, we have to calculate the resistance of the bulb when it is glowing and for that we use Ohm’s law.
\[
  V = I \times R \\
  \therefore R = \dfrac{V}{I} \\
   \Rightarrow R = \dfrac{4}{{0.4}} \\
   \Rightarrow R = \dfrac{{40}}{4} \\
  \therefore R = 10\Omega \\
 \]
The value for resistance of the bulb when glowing is $10\Omega $ . The reason for the difference in resistance is that the resistance depends upon temperature. As the bulb is glowing, the current flows through the bulb, and the temperature of the bulb increases. Resistance of the filament of the bulb grows with a temperature rise. Hence when it glows, its resistance is more significant than when it is cool.

Additional information:
Ohm's law states that the current I in a resistor is proportional to the potential difference V across it, provided that the temperature of the object is constant. In. equation form, it says. where the proportionality constant R is the resistance of the device.

Note:
Resistance cannot be estimated in an operating circuit, so Ohm's Law is beneficial when it requires to be calculated. Rather than closing off the circuit to determine resistance, a technician can find R using the variation of Ohm's Law.