Current Electricity | Electrical Power | AC and DC

Current Electricity - Electrical Power

current electricity electrical power is explained with formula sheets, derivations, DC power, AC average power, power factor, Joule heating, maximum power transfer, electricity bill numericals, SVG graphs and exam-level practice for CBSE Class 12, NEET, JEE Main, JEE Advanced, AP, IB, IGCSE, A-Level and Olympiad Physics.

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1. Formula Sheet First

P = W/tPower is rate of energy consumption.

P = VIElectrical power in a circuit.

P = I²RPower dissipated in resistance using current.

P = V²/RPower in voltage-resistance form.

W = PtEnergy consumed by a device.

W = VItEnergy in voltage-current-time form.

W = I²RtEnergy converted to heat in a resistor.

W = V²t/REnergy using voltage and resistance.

1 kWh = 3.6 × 10⁶ JCommercial energy conversion.

P_dc = VIPower in a DC circuit.

p = viInstantaneous AC power.

P_avg = V_rmsI_rmscosφAverage AC power.

P_R = V_rmsI_rmsPure resistor AC power.

P_L = 0, P_C = 0Pure inductor/capacitor average power.

cosφ = R/ZPower factor of an LCR circuit.

Symbols: P = power in watt, W = energy in joule, V = voltage, I = current, R = resistance, t = time, φ = phase angle, Z = impedance, cosφ = power factor.

Physical meaning: Power tells how fast electrical energy is converted. A 1000 W device consumes energy faster than a 100 W device.

2. What Is Electrical Power?

Electrical power is the rate at which electrical energy is consumed, supplied or converted by a circuit element. It links energy with time and tells how quickly a device works.

Watt: 1 W means 1 joule of energy is converted per second.

Kilowatt: 1 kW = 1000 W, commonly used for heaters, motors and household loads.

Commercial unit: Electricity bills measure energy, not power, in kWh or units.

3. Derivation of Electrical Power

P = W/t and P = VI

By definition, power is work done per unit time: P = W/t.

Electrical work is W = VQ.

Since Q = It, W = VIt. Therefore P = W/t = VI.

P = I²R and P = V²/R

Using V = IR in P = VI gives P = I²R.

Using I = V/R in P = VI gives P = V²/R.

4. Electrical Power in DC Circuits

In DC circuits, voltage and current are steady in direction. For a resistor, power is continuously dissipated as heat according to P = VI = I²R = V²/R.

Battery and load: Source power is delivered to the external load and lost partly in internal resistance.

Wire loss: Power loss in transmission wires is I²R, so high current produces more heating loss.

Example: A 12 V device drawing 2 A consumes P = VI = 24 W.

5. Electrical Power in AC Circuits

In AC, voltage and current vary with time. Instantaneous power is p = vi, while useful average power is P_avg = V_rmsI_rmscosφ.

Average AC Power

Let voltage and current have phase difference φ.

Average over one cycle gives P_avg = V_rmsI_rmscosφ.

cosφ is the power factor and decides how much apparent power becomes useful active power.

Pure resistor: φ = 0, cosφ = 1, so Pavg = Vrms Irms.

Pure inductor: φ = 90°, average power = 0.

Pure capacitor: φ = 90°, average power = 0.

LCR circuit: Pavg = Vrms Irms cosφ and cosφ = R/Z.

Active power: Useful consumed power in watt.

Reactive/apparent power: Important in AC systems and power factor correction.

6. Comparison of AC Power and DC Power

Point	DC Power	AC Power
Voltage type	Constant polarity.	Alternating polarity.
Current type	Steady direction.	Alternating direction.
Formula	P = VI.	Pavg = Vrms Irms cosφ.
Phase difference	Usually no phase concept for simple DC.	Very important.
Power factor	Not required in basic DC.	cosφ controls useful power.
Applications	Batteries, electronics, DC motors.	Homes, generators, transformers.
Exam importance	Circuit power and heating.	RMS, phase and average power.

7. Joule Heating and Power

Joule heating connects energy and power: H = I²Rt and P = H/t = I²R.

Heater: high resistance converts electrical energy to heat.

Fuse: melts due to excessive I²R heating and protects circuits.

Transmission lines: loss is I²R, so lower current reduces power loss.

8. Maximum Power Transfer Concept

For a source with internal resistance r connected to load resistance R, maximum power is delivered to the load when R = r. This is a key JEE-level result.

Condition: Load resistance equals internal resistance.

Efficiency point: Maximum power transfer does not mean maximum efficiency; at R = r, efficiency is 50%.

9. Household Power and Electricity Bill

Appliance rating tells power consumption. Electricity bill is calculated from energy in kWh.

Example 1: A 1000 W iron used for 2 h consumes 1 kW × 2 h = 2 units.

Example 2: A 60 W bulb used for 10 h consumes 0.06 × 10 = 0.6 unit.

10. Graphs and Diagrams

11-17. Exam Question Bank With Accordion Solutions

Click any question to open the answer and explanation.

18. Common Student Mistakes

19. Final Revision Sheet

DC: P = VI = I²R = V²/R.

AC: Pavg = Vrms Irms cosφ.

Pure L/C: Average power is zero.

Power factor: cosφ = R/Z.

Energy: W = Pt and 1 kWh = 3.6 × 10⁶ J.

Trap: Use RMS values in AC average power.

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