4.4.5 Energy Transfer

• E.m.f is defined as the energy transferred by the power supply per unit charge
• This energy transformed is also equal to the work done by the moving charge
• This is defined by the equation:

W = εQ

• Where:
  • W = work done / energy transferred (J)
  • ε = e.m.f (V)
  • Q = charge (C)

• The potential difference is the energy transferred to the electrical component per unit charge
• This means the equation can also be written as:

W = VQ

• Where:
  • V = potential difference (V)

• These equations show that

1 V = 1 J C^-1

Step 1: List the known quantities

• • Energy transferred (work done), W = 0.4 MJ = 0.4 × 10⁶ J
  • E.m.f, ε = 230 V

Step 2: Write the relevant equation

W = εQ

Step 3: Rearrange for charge, Q

Q = W ÷ ε

Step 4: Substitute in the values

Q = (0.4 × 10⁶) ÷ 230 = 1739.13 = 1700 C

• A dynamo or battery transfer energy to each charge carrier, which are electrons in metals, as they pass through
  • Each electron has a charge of e

• Since the energy transferred (work done) W is defined as

W = QV

• Then:

W = eV

• Where the charge Q is now replaced with the charge of the electron e
• 1 eV is 1 electronvolt, which is defined as:

A unit of energy equal to the work done by an electron accelerated through a potential difference of 1 volt

• When a potential difference is applied across a conductor, the electrons are accelerated and gain kinetic energy

Electron beam accelerated through a potential difference of 1 V

• This kinetic energy gained is equal to an electronvolt:

eV = ½ mv²

• Where:
  • e = elementary charge (C)
  • V = potential difference (V)
  • m = mass of the electron (kg)
  • v = speed of the electrons (m s^-1)

• To convert between eV and J:
  • eV → J: multiply by 1.6 × 10^-19
  • J → eV: divide by 1.6 × 10^-19