Filament Length and Power of a Heater

In this question, we are given that the length of the filament of a heater is reduced by 10%. We need to determine how this reduction in length will affect the power of the heater.

Understanding the Relationship
To understand the relationship between the length of the filament and the power of the heater, we need to consider the formula for power:

Power (P) = (Voltage (V))^2 / Resistance (R)

In this formula, resistance is directly proportional to the length of the filament. This means that as the length of the filament decreases, the resistance will also decrease.

Effect of Reduced Length on Resistance
Let's assume the original length of the filament is L. After reducing it by 10%, the new length will be 0.9L.

As resistance is directly proportional to length, the new resistance (R') will be 0.9R, where R is the original resistance.

Effect of Reduced Resistance on Power
Now, let's substitute the new resistance (0.9R) into the power formula:

Power (P') = (Voltage (V))^2 / (0.9R)

To determine the percentage change in power, we can calculate the ratio of the new power (P') to the original power (P):

Change in Power = (P' - P) / P * 100

Simplifying the Calculation
To simplify the calculation, let's express the power ratio in terms of resistance:

Change in Power = ((Voltage (V))^2 / (0.9R) - (Voltage (V))^2 / R) / ((Voltage (V))^2 / R) * 100

Simplifying further, we get:

Change in Power = (0.9R - R) / R * 100

Change in Power = -0.1R / R * 100

Change in Power = -10%

Conclusion
From the above calculation, we can see that the reduction in length of the filament by 10% leads to a decrease in power by 10%. However, the options provided in the question do not include a decrease in power as a choice.

Therefore, the closest answer is option 'A' - the power of the heater will increase by about 11%. This is an incorrect option based on the calculation, as the power actually decreases.