Overview
This lecture covers circuit analysis using Ohm's Law, power calculations, energy usage billing, and efficiency in electrical systems through practical example problems.
Ohm's Law and Current Calculation
- Ohm's Law: V = I × R, where V is voltage, I is current, R is resistance.
- To find current: I = V / R.
- Example: For V = 16 V and R = 2,000 Ω, I = 0.008 A or 8 mA.
Power Calculation
- Power formula: P = V × I, where P is power in watts.
- Example: For V = 120 V and I = 5 A, P = 600 W.
Using VI Relationships and Resistance
- For given voltage and current, power: P = V × I.
- Example: With V = 120 V and I = 0.625 A, P = 75 W.
- Resistance formula: R = V / I.
- Example: R = 120 V / 0.625 A = 192 Ω.
Energy Usage and Billing
- Energy usage (in kilowatt-hours) = current meter reading − previous reading.
- Example: 5,360 kWh − 4,650 kWh = 710 kWh used.
- Cost = energy used × unit cost.
- Example: 710 kWh × $0.11 = $78.10.
Motor Efficiency and Input Power
- Efficiency formula: efficiency = output power / input power.
- To get input power: input = output / efficiency.
- Convert horsepower to watt (1 HP = 746 W), so 2 HP = 1,492 W.
- If efficiency = 75%, input = 1,492 W / 0.75 ≈ 1,989 W.
- To find current: I = P / V.
- Example: I = 1,989 W / 220 V ≈ 9 A.
System Efficiency (Cascaded Components)
- Overall efficiency = efficiency₁ × efficiency₂ × efficiency₃.
- Multiply component efficiencies (as decimals) to get total system efficiency.
Key Terms & Definitions
- Ohm's Law — V = I × R, relation between voltage, current, and resistance.
- Power (P) — Rate at which energy is used, P = V × I.
- Resistance (R) — Opposition to current, measured in ohms (Ω).
- Efficiency — Ratio of output power to input power, usually as a percent.
- Kilowatt-hour (kWh) — Unit of energy consumption.
Action Items / Next Steps
- Practice similar circuit and power problems.
- Review assigned textbook sections on Ohm's Law, power, and efficiency.
- Prepare questions for clarification on next class.