A video game console operates potential difference of 12.00 V as shown in fig. The potential difference supplied by the power receptacle is 120 V AC. A transformer is used to convert one voltage to the other. If the secondary coil of the transformer (the 12.00 V side) has 1200 loops, how many loops does the primary coil have?
In a transformer, the ratio of the voltages on either side is directly proportional to the ratio of the number of loops.
=> V1/N1 = V2/N2
In this case, V1 = 12V, N1 = 1200, V2 = 120V
=> 12/1200 = 120/N2
=> N2 = 12,000
Within a magnetic core magnetic flux occurs. The flux is dependent on the primary current, and the primary turns
Ip*Np. This same flux flows in the core of the secondary, Is*Ns
so IpNp=Is*Ns
now on voltage, in accordance with Lenz's law, this flux causes in each turn, an induced voltage. so the total induced voltage is k*voltage/turn*turns *flux
Vs=kNs*flux
or Vs/Ns=k*flux. But on the primary, the same constant k isoccuring in generating the flux, so
Vs/Ns=Vp/Np
or
Vp/Vs=Np/Ns
120/12=1200/Ns
or Ns=12,000 turns.
To determine the number of loops in the primary coil, we can use the formula for the turns ratio of a transformer:
Turns ratio = number of turns in the secondary coil / number of turns in the primary coil
In this case, the turns ratio is given by:
Turns ratio = 12.00 V / 120 V = 0.1
Since the turns ratio is equal to the ratio of the number of turns, we have:
0.1 = number of turns in the secondary coil / number of turns in the primary coil
Now, let's solve for the number of turns in the primary coil:
number of turns in the primary coil = number of turns in the secondary coil / 0.1
number of turns in the primary coil = 1200 / 0.1
number of turns in the primary coil = 12,000
Therefore, the primary coil of the transformer has 12,000 loops.