Transformer

V_P  :  V_S  = N_P :  N_S

• V_P   voltage across the primary coil in V
• V_S    voltage induced in the secondary coil in V
• N_P    amount of turns in the primary coil
• N_S    amount of turns in the secondary coil                                        

P_P = P_S      (Assuming 100 % energy transfer, no energy dissipated in heating)

V_P I_P = V_S I_S

• P_P    power of the primary coil W (of VA)
• I_P     current in the primary coil in A
• P_S      power of the secondary coil  in W (of VA)
•  I_S       current  in the secondary coil  in A

Examples

1.   The primary coil of a transformer consists of 400 turns. The secondary coil  

      80 turns.

      The voltage across the primary coil is 230 V

      Find the voltage across the secondary coil

      V_P  :  V_S  = N_P :  N_S

      230 : V_S = 400 : 80

      230 : V_S = 5 : 1

      5 V_s = (230)(1)

      V_S = 230/5 = 46 V

2.    The primary coil is connected with an AC source

A bulb is connected with the secondary coil.

The voltage across the bulb is 6.0 V and

the current through the bulb is  0.4 A

The turns ratio is 5:1

 (N_P : N_S  = 5: 1)

Calculate the current in the primary coil

        P_S = V_S I_S = (6.0)( 0.4) = 2.4 W

        V_P = 5 V_S = (5 )(6.0) = 30 V

        P_P = P_S = 2.4 W

        P_P = V_P I_P

             2.4 = 30 I_P

             I_P = 2.4/30 = 0.8 A