Energy Transfers in Electrical Systems (P2.4)

Electrical power

Power is the rate of energy transfer:

P = IV   and   P = I²R   and   P = V²/R

P = power (W), I = current A, V = p.d. (V), R = resistance (Ω).

Worked example: A 230 V toaster draws 4 A. P = IV = 230 × 4 = 920 W.

Energy in everyday appliances

E = Pt   (or E = IVt)

E = energy (J), P = power (W), t = time (s).

Also: E = QV (energy = charge × p.d.) — energy transferred when charge Q flows through p.d. V.

kilowatt-hours (kWh): a practical unit of electrical energy.
1 kWh = 1 kW used for 1 hour = 1,000 W × 3,600 s = 3,600,000 J = 3.6 MJ.

Cost of electricity:

Cost = power (kW) × time (hours) × price per kWh

Example: A 2 kW heater used for 3 hours at 25p/kWh: Cost = 2 × 3 × 0.25 = £1.50.

The National Grid

The National Grid transmits electricity at very high voltages (400 kV) from power stations to homes.

Why high voltage?
At high voltage, current is low (P = IV; same P, high V → low I). Lower current → less energy wasted as heat in cables (P_wasted = I²R). At low voltage, high current → massive I²R losses.

Transformers (step-up and step-down):

• Step-up transformer: increases voltage (e.g. from ~25 kV at power station to 400 kV for transmission).
• Step-down transformer: decreases voltage (e.g. from 400 kV to 230 V for homes).

Transformers only work with ac — the changing magnetic field is essential for induction.

P_primary = P_secondary (ideal transformer: no energy lost):

V_p / V_s = N_p / N_s   (and   V_p × I_p = V_s × I_s)

Common exam errors

1. Using P = IV with dc units when the supply is ac — for ac, P = V_rms × I_rms (but at GCSE, treat the formula as P = IV with given values).
2. Forgetting to convert minutes to seconds (or hours to seconds) in E = Pt.
3. Saying step-up transformers increase power — they increase voltage at the expense of current; power is conserved (approximately).