MCQ Detailed View

If the length of a heater coil is reduced by 10%, the power consumed will increase by more than 10%. To understand why, let’s look at the basic formula in simple terms.

The power used by an electric heater is given by the formula:
P = V² / R
Where:
- P is power,
- V is voltage,
- R is resistance.

Now, resistance (R) of a coil is directly proportional to its length. This means:
- If you decrease the length of the coil, its resistance becomes lower.
- Lower resistance allows more current to flow, which increases the power consumption.

So, when you reduce the length of the coil by 10%, the resistance becomes less. This reduced resistance causes a sharp increase in power. However, the increase in power is not just 10%, it’s **more than 10%**, because power is inversely related to resistance and changes non-linearly.

Let’s understand with an example:
- Suppose the original resistance is 100 ohms.
- Reducing the coil by 10% brings resistance to around 90 ohms.
- Using the formula, the new power is V² / 90 compared to the old V² / 100.
- That’s an increase of more than 10% in power!

✅ Therefore, the correct answer is: Increase over 10%.