Transformer Equations (AQA GCSE Physics)

• The output potential difference (voltage) of a transformer depends on:
  • The number of turns on the primary and secondary coils
  • The input potential difference (voltage)

• It can be calculated using the equation:

• This equation can be written using symbols as follows:

• Where
  • V_p = potential difference (voltage) across the primary coil in volts (V)
  • V_s = potential difference (voltage) across the secondary coil in volts (V)
  • n_p = number of turns on primary coil
  • n_s = number of turns on secondary coil

• The equation above can be flipped upside down to give:

• The equations above show that:
  • The ratio of the potential differences across the primary and secondary coils of a transformer is equal to the ratio of the number of turns on each coil

Step-up Transformer

• A step-up transformer increases the potential difference of a power source
• A step-up transformer has more turns on the secondary coil than on the primary coil (N_s > N_p)

Step-down Transformer

• A step-down transformer decreases the potential difference of a power source
• A step-down transformer has fewer turns on the secondary coil than on the primary coil (N_s < N_p)

• An ideal transformer would be 100% efficient
  • Although transformers can increase the voltage of a power source, due to the law of conservation of energy, they cannot increase the power output

• If a transformer is 100% efficient:

Input power = Output power

• The equation to calculate electrical power is:

P = V × I

• Where:
  • P = power in Watts (W)
  • V = potential difference in volts (V)
  • I = current in amps (A)

• Therefore, if a transformer is 100% efficient then:

V_p × I_p = V_s × I_s

• Where:
  • V_p = potential difference across primary coil in volts (V)
  • I_p = current through primary coil in Amps (A)
  • V_s = potential difference across secondary coil in volts (V)
  • I_s = current through secondary coil in Amps (A)

• The equation above could also be written as:

P_s = V_p × I_p

• Where:
  • P_s = output power (power produced in secondary coil) in Watts (W)

Step 1: List the known quantities

• • Voltage in primary coil, V_p = 115 V
  • Voltage in secondary coil, V_s = 230 V
  • Current in secondary coil, I_s = 5 A

Step 2: Write the equation linking the known values to the current drawn from the supply, I_p

V_p × I_p = V_s × I_s

Step 3: Substitute in the known values

115 × I_p = 230 × 5

Step 4: Rearrange the equation to find I_p

Step 5: Calculate a value for I_p and include the correct unit

I_p = 10 A