A model electric train requires 12 V to operate. When connected to a household voltage of 120 V, a transformer is needed. If the primary coil has 500 turns, how many turns must the secondary coil have?

(12/120) * 500

To determine the number of turns the secondary coil must have, we can use the turns ratio equation:

N₁/N₂ = V₁/V₂

Where:
N₁ = number of turns in the primary coil
N₂ = number of turns in the secondary coil
V₁ = voltage across the primary coil
V₂ = voltage across the secondary coil

We know:
V₁ = 120 V (household voltage)
V₂ = 12 V (required voltage for the train)

Substituting the known values into the equation:

500/N₂ = 120/12

Next, we can simplify and solve for N₂:

500/N₂ = 10

To isolate N₂, we can cross-multiply:

N₂ * 10 = 500

Dividing both sides by 10:

N₂ = 500/10

N₂ = 50

Therefore, the secondary coil must have 50 turns in order to operate the model electric train with a household voltage of 120 V.