If a 220 V heater is connected to 110 V supply, then power consumed by it:

Explanation:

Power Consumption of a Heater:

Problem Statement: If a 220 V heater is connected to a 110 V supply, then power consumed by it: 1) will be the same, 2) will reduce by 1/2, 3) will reduce to 1/4, 4) will be doubled.

Correct Option: Option 3 (will reduce to 1/4)

To understand why the power consumed by a 220 V heater will reduce to 1/4 when connected to a 110 V supply, we need to delve into the principles of electrical power consumption and the relationship between voltage, current, and resistance.

Important Formulas:

• Ohm's Law: $V = I \times R$ , where $V$ is the voltage, $I$ is the current, and $R$ is the resistance.
• Power: $P = V \times I$ (Power can also be expressed as $P = I^2 \times R$ or $P = \frac{V^2}{R}$ ).

Detailed Explanation:

When a heater is designed for 220 V, it means that the heater is expected to operate optimally at this voltage. Let's denote:

• $V_1 = 220$ V (initial voltage)
• $V_2 = 110$ V (reduced voltage)

Let's assume that the resistance $R$ of the heater remains constant (which is a valid assumption as the resistance of a heater, primarily made of metallic elements, doesn't change significantly with voltage).

Initial Power Consumption:

Using the power formula $P = \frac{V^2}{R}$ :

• $P_1 = \frac{V_1^2}{R}$
• $P_1 = \frac{(220)^2}{R}$

Power Consumption at 110 V:

Now, when the voltage is reduced to 110 V:

• $P_2 = \frac{V_2^2}{R}$
• $P_2 = \frac{(110)^2}{R}$

To find the ratio of the new power consumption to the initial power consumption:

• $\frac{P_2}{P_1} = \frac{\frac{(110)^2}{R}}{\frac{(220)^2}{R}}$
• $\frac{P_2}{P_1} = \frac{110^2}{220^2}$
• $\frac{P_2}{P_1} = \frac{12100}{48400}$
• $\frac{P_2}{P_1} = \frac{1}{4}$

Therefore, $P_2 = \frac{P_1}{4}$ .

This calculation shows that the power consumed by the heater when connected to a 110 V supply will be one-fourth of the power consumed at 220 V. Hence, the correct answer is that the power will reduce to 1/4.

Correct Option Analysis:

The correct option is:

Option 3: will reduce to 1/4.

This option is correct because when the voltage is halved from 220 V to 110 V, the power consumed by the heater reduces to a quarter of its original power consumption.

Additional Information

Analysis of Other Options:

To further understand the analysis, let’s evaluate the other options:

Option 1: will be the same.

This option is incorrect because the power consumed by an electrical device is dependent on the voltage supplied to it. When the voltage is halved, the power consumption cannot remain the same. Using the formula $P = \frac{V^2}{R}$ , it is evident that reducing the voltage will reduce the power consumption.

Option 2: will reduce by 1/2.

This option is also incorrect because if the voltage is halved, the power consumption does not reduce by half. It actually reduces to a quarter, as shown in the detailed explanation using the power formula.

Option 4: will be doubled.

This option is incorrect because reducing the voltage cannot result in an increase in power consumption. In fact, power consumption decreases when the voltage is reduced, as demonstrated by the formula $P = \frac{V^2}{R}$ .

Conclusion:

Understanding the relationship between voltage, current, and power is essential for correctly analyzing the power consumption of electrical devices. When the voltage supplied to a heater is reduced from 220 V to 110 V, the power consumed by the heater reduces to one-fourth of its original consumption. This conclusion is based on the power formula $P = \frac{V^2}{R}$ , which shows a quadratic relationship between voltage and power.