Case Study:

During winter in northern India, electric heaters are commonly used in households. In a home in Meerut, a family uses a 220 V electric heater rated at 1100 W to keep their room warm.

The heater contains a high-resistance nichrome wire that converts electrical energy into heat based on Joule’s law. When connected to the power supply, the current flowing through the heater can be calculated using the power formula:

P = V² / R

Rearranging, the resistance of the heater is:
R = V² / P = (220)² / 1100 = 44 Ω

The current drawn by the heater is:
I = P / V = 1100 / 220 = 5 A

The family noticed that when voltage fluctuated during peak hours (dropping to 200 V), the heater produced less heat. This is because power depends on the square of voltage, and a decrease in voltage significantly reduces heat output.

Additionally, continuous use of the heater increased electricity bills. For example, using the heater for 5 hours daily consumed:
Energy = 1100 W × 5 h = 5500 Wh = 5.5 kWh per day

This case highlights the importance of resistance, voltage, and power relationships in everyday electrical appliances and emphasizes energy-efficient usage in Indian households.

Questions:

Section A - MCQs

1. Why is nichrome wire used in electric heaters?

A. It has low resistance
B. It has high resistance and high melting point
C. It conducts electricity poorly
D. It reduces voltage

2. What is the resistance of the heater?

A. 22 Ω
B. 44 Ω
C. 110 Ω
D. 220 Ω

3. Why does the heater produce less heat at 200 V?

A. Resistance increases
B. Current increases
C. Power decreases due to lower voltage
D. Wire melts

4. What is the daily energy consumption if the heater runs for 5 hours?

A. 2.2 kWh
B. 3.3 kWh
C. 5.5 kWh
D. 11 kWh

Section B - Short Answer Questions

1. Calculate the current drawn by the heater.

2. Explain how voltage affects heat production in an electric heater.

3. Why does prolonged use of heaters increase electricity bills?

Section C - Long Answer Question

1. If the voltage increases to 240 V, how will the power consumption and heat output change? Calculate the new power and analyze its impact on the heater and electricity usage.

Answer Key:

Section A - MCQs Answers:

1. B
2. B
3. C
4. C

Section B - Short Answers:

1. I = P / V = 1100 / 220 = 5 A

2. Heat produced depends on power (P ∝ V²). A decrease in voltage reduces power significantly, leading to less heat generation.

3. Heaters consume high power; longer usage increases total energy consumption (kWh), leading to higher electricity bills.

Section C - Long Answer:

• New voltage = 240 V
• Resistance = 44 Ω

New power:
P = V² / R = (240)² / 44 = 57600 / 44 ≈ 1309 W

Analysis:

• Power increases --> more heat produced
• Higher electricity consumption
• May reduce heater lifespan due to overheating
• Increases electricity cost