Transformer Equations | Physics for Grade 10 PDF Download

The Transformer Equation

• 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)

Exam Tip

1. When you are using the transformer equation make sure you have used the same letter (p or s) in the numerators (top line) of the fraction and the same letter (p or s) in the denominators (bottom line) of the fraction. 
2. There will be less rearranging to do in a calculation if the variable which you are trying to find is on the numerator (top line) of the fraction.
3. The individual loops of wire going around each side of the transformer should be referred to as turns and not coils.

The Ideal Transformer Equation

• 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)

Solved Example

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