IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Resistance of a Bulb

## Introduction

In many of the textbook numerical, the resistance of a bulb is asked if the voltage and power are given. The relevant equation is $$P=V^2/R$$.

However, if you measure the resistance directly with a meter, it turns out to be different. Some times it is said that if the voltage applied is less, what will be the power. This is also not solvable using $$P=V^2/R$$.

## Apparatus

A 100 W bulb, a multimeter, a scooter bulb, 6-0-6 transformer, 2 multimeters

## Procedure

### Part A

1. Look at the stamp on the bulb. It is 100 W, 230 V. Calculate the resistance of the bulb using these data.
2. Put the multimeter in resistance mode. Touch the ends of the bulb filament to the multimeter leads and measure the resistance. Why does the measured resistance different from the one calculated above?
3. The temperature coefficient of tungsten is 0.0045/K. Assuming this to be independent of temperature, estimate the temperature of the filament when the bulb is connected to a 230 V source.

### Part B

1. Arrange the circuit as shown. Use multimeter in AC voltage mode across the bulb and in AC current mode to measure the current going through the bulb.
2. On the secondary side, you will find three terminals (A,O,B). Use the end terminals to take power. For 6-0-6 transformer, this means you are taking 12 V from the transformer.
3. Connect the free ends to complete the circuit. Measure V and I, and from that calculate the resistance of the bulb. Write in the table.
4. Now repeat the exercise using terminal O and B on the transformer. This ensures that you are using 6 V AC from the transformer. Now get, $$V$$ and $$R$$ and fill the table.

## Discussion

The resistance of the coil depends on temperature and increasing voltage across the filament increases its temperature. Hence $$V\propto I$$ does not hold. By raising the temperature we provide more kinetic energy to the free electrons and that increases the collisions/scattering from different scattering centers. This is responsible for increase in resistance.

## Note

Figure and tables to be made