Ohm's Law, Power and Energy
The V = IR relationship, power in all four forms, and energy accounting.
- Apply Ohm's law to find V, I or R in simple branches
- Compute electrical power using VI, I²R or V²/R
- Distinguish energy (kWh) from power (kW) in practical problems
Your hostel electricity bill is energy in kWh; the geyser rating plate is power in kW. Confusing the two is the most common first-year mistake — and it costs marks every exam season.
Ohm's law (linear, passive sign convention): V = I·R when temperature and material properties are constant. Applies to resistors, not to diodes or non-linear devices.
Passive sign convention: current enters the + terminal of a passive element. Power P = V·I > 0 means the element absorbs power; P < 0 means it supplies.
Power forms: P = VI = I²R = V²/R — pick the form that has the known quantities. Maximum power transfer and heating problems almost always want I²R.
Energy: W = P·t. In utility billing, W is in kilowatt-hours: a 2 kW geyser running 1.5 h consumes 3 kWh.
| Knowns | Use | Typical use |
|---|---|---|
| V and I | P = VI | General branch power |
| I and R | P = I²R | Heating, I²R losses |
| V and R | P = V²/R | Fixed-voltage heating elements |
V in volts, I in amperes, R in ohms, P in watts, W in joules or Wh. Convert kW to W before applying formulas.
- 1
Convert time
45 min = 0.75 h.
- 2
Energy in kWh
W = 2 kW x 0.75 h = 1.5 kWh.
- 3
Convert to joules
1.5 kWh x 3.6e6 J/kWh = 5.4e6 J.
Solution
1.5 kWh = 5.4 MJ.
A 60 W bulb operates at 230 V. Find its resistance.
Hint: R = V²/P.
Applying Ohm’s law to a diode
Ohm’s law is linear; non-linear devices need their V-I characteristic.
Mixing kW and W in bill problems
Convert everything to kW before multiplying by hours if the answer should be kWh.
State the passive sign convention and the meaning of P > 0.
Current enters the + terminal; P > 0 means the element absorbs power.
Source: Standard first-question of BEE papers.
- V = IR for linear resistors; P = VI = I²R = V²/R.
- Positive absorbed power under passive sign convention.
- Energy = power x time; utility bills use kWh.
