Transformer Calculations (CIE IGCSE 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

EXTENDED

• 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

• Transformers have a number of roles:
  • They are used to increase the potential difference of electricity before it is transmitted across the national grid
  • They are used to lower the high voltage electricity used in power lines to the lower voltages used in houses
  • They are used in adapters to lower mains voltage to the lower voltages used by many electronic devices

Advantages of High Voltage Transmission

• When electricity is transmitted over large distances, the current in the wires heats them, resulting in energy loss
• To transmit the same amount of power as the input power the potential difference at which the electricity is transmitted should be increased
  • This will result in a smaller current being transmitted through the power lines
  • This is because P = IV, so if V increases, I must decrease to transmit the same power

• A smaller current flowing through the power lines results in less heat being produced in the wire
  • This will reduce the energy loss in the power lines

Electricity is transmitted at high voltage, reducing the current and hence power loss in the cables

EXTENDED

• When a current passes through a wire, the current creates a heating effect which means the wires warm up
• This means they lose electrical energy as heat which reduced the efficiency of the transformer
  • This is due to electrical resistance which is present in all wires

• The power (energy per second) lost in the wire is given by the following equation

P = I²R

• Where:
  • P = power in watts (W)
  • I = current in amps (A)
  • R = resistance in ohms (Ω)

• Since the power is the energy lost per second, the total energy lost in a time t will be:

E = P × t

• Where:
  • E = energy in joules (J)
  • t  = time in seconds (s)

• A step-up transformer may be used to increase the voltage of a power supply from the power station to the transmission wires
• The number of turns and voltage for the transformer is related by the following equation:

•  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 the primary coil
  • n_s = number of turns on the secondary coil

• A step-up transformer has more turns on the secondary coil, N_s, than on the primary coil, N_p
• Since a transformer cannot output more power than is put into it, increasing the voltage must result in the current being lowered

I_pV_p = I_sV_s

• Where:
  • I_p = current in the primary coil in amps (A)
  • I_s = current in the secondary coil in amps (A)

• Lower current results in less power and energy loss in the cables
  • This makes the transfer of electrical energy through the wires more efficient