Edexcel A Level (IAL) Physics-2.38 Electrical Power- Study Notes- New Syllabus

Electrical Power and Energy: \( P = VI \), \( W = VIt \) and Related Equations

In electrical circuits, power measures the rate at which energy is transferred. Using basic definitions of voltage and current, we derive several useful power equations.

 Definition of Electrical Power

Power is the rate of doing work or transferring energy:

\( P = \dfrac{W}{t} \)

• \( P \) = power (watts, W)
• \( W \) = energy transferred (joules, J)
• \( t \) = time (s)

Deriving \( P = VI \)

Voltage is energy transferred per coulomb:

\( V = \dfrac{W}{Q} \)

Current is charge per second:

\( I = \dfrac{Q}{t} \)

Substitute into the power formula:

\( P = \dfrac{W}{t} = \dfrac{VQ}{t} = VI \)

Thus:

\( P = VI \)

Energy Transfer in a Circuit: \( W = VIt \)

Using \( P = VI \) and \( P = \dfrac{W}{t} \):

\( W = P t = (VI)t = V I t \)

This gives the total energy transferred over time.

Deriving \( P = I^{2}R \)

Use Ohm’s law: \( V = IR \). Substitute into \( P = VI \):

\( P = (IR)I = I^{2} R \)

This shows power increases with square of current for a resistor.

Deriving \( P = \dfrac{V^{2}}{R} \)

Again from \( P = VI \) but substitute \( I = \dfrac{V}{R} \):

\( P = V \left( \dfrac{V}{R} \right) = \dfrac{V^{2}}{R} \)

Useful when voltage and resistance are known.

Summary of Useful Power Equations