Electric Circuits Power and Energy Quiz

Power and Energy in Electric Circuits

• Power is defined as the rate at which work is done, measured in watts (W) or joules per second (J/s).
• Energy represents the capacity to perform work, measured in joules (J) or kilowatt-hours (kWh).
• Key formulas:
  • Power: P = V × I (Voltage × Current)
  • Energy: E = P × t (Power × Time)

Units of Measurement

• Power: Measured in watts (W)
• Energy: Measured in joules (J) or kilowatt-hours (kWh)
• 1 kilowatt (kW) is equivalent to 1000 watts (W).

Practical Application of Power and Energy Formulas

• Calculate power in a circuit with:
  • P = V² / R (Voltage squared divided by Resistance)
  • P = I² × R (Current squared times Resistance)
• Energy consumption in kilowatt-hours can be calculated from power and time.

Energy Consumption in Households

• Common unit of energy consumption is the kilowatt-hour (kWh).
• Calculation example:
  • For a 1000 W appliance running for 10 hours:
    • E = P × t = 1000 W × 10 h = 10 kWh

Cost of Electrical Energy

• Electrical bill calculated as:
  • Cost ()=EnergyConsumed(kWh)×Rate() = Energy Consumed (kWh) × Rate ()=EnergyConsumed(kWh)×Rate(/kWh)

Worked Examples

• Example: A 1000 W heater on for 10 hours:
  • Energy in joules: E = 1000 W × (10 × 3600) s = 36,000,000 J
  • Energy in kWh: 10 kWh.
• Refrigerator Calculation (2 kW usage):
  • Monthly energy: E = 2 kW × 24 h/day × 30 days = 1440 kWh.

Energy Efficiency Practices

• Set computers to ‘Sleep’ or ‘Hibernate’ modes to reduce power consumption.
• Properly maintain appliances to ensure efficient operation:
  • Check seals on ovens.
  • Use correct water levels for washing machines.
• Use energy-efficient appliances, indicated by energy labels.

Energy-Saving Tips

• Replace incandescent bulbs with energy-saving options like LEDs.
• Switch off lights and appliances when not in use.
• Control air conditioner temperature settings for better efficiency.

Appliance Ratings

• Voltage rating indicates the voltage an appliance is designed for, e.g., bulbs (60 W, 230 V; 40 W, 230 V), fluorescent lamps (32 W, 230 V), and water heaters (3000 W, 230 V).
• Power rating reflects how much energy an appliance uses; a 60 W bulb is brighter compared to a 40 W bulb due to higher work done per unit time.

Electricity and Energy Calculation

• Rated current calculation for a 60 W, 230 V bulb:
  • Current (I) = Power (P) / Voltage (V) = 60 W / 230 V = 0.26 A.
• Resistance (R) is calculated using Ohm's law: R = V / I = 230 V / 0.26 A = 884.6 Ω.

Energy Usage

• Energy (E) is measured in joules (J) or watt-seconds (Ws); large energy uses in households are more conveniently expressed in kilowatt-hours (kWh).
• Conversion: 3,600,000 J = 1 kWh.
• Energy consumption formula: E = P × t, where P = power in kW and t = time in hours.

Cost Calculation of Appliance Usage

• Example for a 900 W heater used for 30 minutes daily over a week:
  • E = 0.9 kW × 0.5 h × 7 days = 3.15 kWh, costing $0.79 at $0.25 per kWh.

Utility Bills Overview

• Households typically receive bills for electricity, gas, and water services.
• Example bill includes 229 kWh usage yielding a charge of $51.32 at a rate of $0.2241 per kWh.

High-Energy Consumption Appliances

• Common high-energy appliances: refrigerator, air conditioner, water heater, and electric iron.
• Appliances with higher power ratings consume more energy.

Energy Consumption Reduction Strategies

• Unplug unused chargers and switch off power supply to appliances.
• Enable 'sleep' and 'hibernate' modes on computers to save energy.
• Optimal temperature settings can reduce air conditioning energy use.
• Efficient appliance use includes checking seals on ovens and washing machines to match load sizes.
• Purchasing energy-efficient appliances can lead to long-term savings.

Energy-Saving Tips

• Replace incandescent bulbs with energy-saving alternatives such as LED bulbs.
• Make it a habit to turn off lights when not in use.

Practice Questions

• Analyze power dissipation in resistors connected to a power supply.
• Determine the energy consumption of appliances based on their power rating and usage duration (e.g., 1 kW refrigerator usage over 30 days).