A soldering iron uses an electric current in a wire to heat the tip. A transformer with 100 turns on the secondary coil provides 54 W at an rms voltage of 26 V.
a) How many turns are in the primary coil?
b) What is the current in the primary coil?
To find the number of turns in the primary coil of a transformer, we need to use the formula for the turns ratio. The turns ratio is given by the ratio of the number of turns in the primary coil (N₁) to the number of turns in the secondary coil (N₂).
a) The turns ratio is given as:
N₁/N₂ = V₁/V₂
where V₁ and V₂ represent the voltages across the primary and secondary coils, respectively.
In this case, we want to find N₁, so rearrange the equation:
N₁ = (N₂ * V₁) / V₂
Given that N₂ = 100 and V₂ = 26 V, substitute these values into the equation along with the voltage across the primary coil V₁.
b) To find the current in the primary coil, we can use the formula:
I₁ = P₁ / V₁
where I₁ represents the current in the primary coil and P₁ represents the power supplied to the primary coil.
Given that P₁ = 54 W and V₁ is unknown, we need to use the power formula P₁ = I₁ * V₁, rearranged to solve for V₁:
V₁ = P₁ / I₁
Substitute the given values to calculate the current in the primary coil.