Current Electricity | Electrical Energy | Power

Current Electricity - Electrical Energy

current electricity electrical energy is explained with formula sheets, derivations, Joule heating, electricity bill numericals, SVG graphs and exam-level practice for CBSE Class 12, NEET, IIT-JEE, JEE Main, JEE Advanced, IB, AP, A-Level and Olympiad Physics.

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1. Formula Sheet First

W = VQElectrical work done when charge Q moves through potential difference V.

W = VItEnergy consumed by a device in time t.

W = I²RtEnergy or heat in a resistor using current.

W = V²t/REnergy in a resistor using voltage.

P = W/tPower is rate of doing electrical work.

P = VIElectrical power delivered to a device.

P = I²RPower dissipated in resistance.

P = V²/RPower in voltage-resistance form.

H = I²RtJoule's law of heating.

1 unit = 1 kWhCommercial unit of electrical energy.

1 kWh = 3.6 × 10⁶ JEnergy conversion for bills.

Cost = Units × RateBasic electricity bill calculation.

Symbols: W = electrical energy/work in joule, V = potential difference in volt, Q = charge in coulomb, I = current in ampere, R = resistance in ohm, t = time in second, P = power in watt, H = heat in joule.

Physical meaning: energy tells how much work is transferred; power tells how fast energy is transferred. Same energy can be used slowly or quickly depending on power rating.

2. What Is Electrical Energy?

Electrical energy is the work done by an electric field in moving charge through a potential difference. In a circuit, the battery supplies energy and appliances convert it into heat, light, sound, motion or chemical energy.

Battery transfer: A battery uses chemical energy to push charge through the circuit. Each coulomb receives energy equal to V joule.

Appliance consumption: A bulb converts electrical energy into light and heat; a heater converts most of it into heat.

Energy conversion: Electrical energy is not destroyed. It changes form according to the device connected in the circuit.

3. Derivation of Electrical Energy

Derivation: W = VQ

Potential difference is work done per unit charge: V = W/Q.

Rearranging gives W = VQ. This is the basic expression for electrical energy.

Derivation: W = VIt

Current is charge per unit time: I = Q/t.

So charge flowing in time t is Q = It.

Substitute in W = VQ: W = VIt.

Derivation: W = I²Rt and W = V²t/R

From Ohm's law, V = IR. Put this in W = VIt to get W = I²Rt.

Also, I = V/R. Put this in W = VIt to get W = V²t/R.

4. Electrical Power

Electrical power is the rate at which electrical energy is consumed or converted by an appliance.

P = W/t. Since W = VIt, P = VI.

Using V = IR, P = I²R.

Using I = V/R, P = V²/R.

Term	Meaning	Example
Watt	SI unit of power. 1 W = 1 J/s.	10 W LED bulb.
Kilowatt	1000 W.	2 kW heater.
Commercial unit	1 kWh is one unit of electricity.	Used in household bills.

5. Joule's Law of Heating

When current flows through a resistance, electrical energy is converted into heat. The heat produced is proportional to square of current, resistance and time.

H = I²RtHeat produced in joule.

H ∝ I²Doubling current makes heat four times.

H ∝ RMore resistance produces more heat for same current.

Electric heater: high-resistance element converts electrical energy into heat.

Fuse wire: melts when excessive current produces too much heat.

Filament bulb: tungsten becomes hot and glows because of Joule heating.

6. Energy Consumption and Electricity Bill

Electricity boards charge energy in kWh. If an appliance of power P kilowatt works for t hours, then energy consumed = P × t kWh.

Example 1: A 100 W bulb runs for 10 h. Energy = 0.1 kW × 10 h = 1 kWh = 1 unit.

Example 2: A 2 kW heater runs for 3 h. Energy = 2 × 3 = 6 units. If rate is Rs. 8/unit, cost = Rs. 48.

7. Graphical and Conceptual Understanding

8-13. Exam Question Bank With Accordion Solutions

Click any question to open the answer and explanation.

14. Common Student Mistakes

15. Final Revision Sheet

Energy: W = VQ = VIt = I²Rt = V²t/R.

Power: P = W/t = VI = I²R = V²/R.

Heating: H = I²Rt. Heat depends most strongly on current because of square relation.

Commercial unit: 1 kWh = 1 unit = 3.6 × 10⁶ J.

Bill method: Units = power in kW × time in hours.

Exam tip: Convert minute/hour into seconds for joule formula and into hours for kWh formula.

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