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 answer these questions, we need to apply the principles of transformers and power calculations.
a) To determine the number of turns in the primary coil, we can use the formula for transformer voltage ratio:
(Vp / Vs) = (Np / Ns)
Where:
Vp = Voltage in the primary coil
Vs = Voltage in the secondary coil
Np = Number of turns in the primary coil
Ns = Number of turns in the secondary coil
From the information given, the voltage in the secondary coil (Vs) is 26V. Since the primary coil supplies power to the secondary coil, the voltage ratio is 1:1. Therefore, the voltage in the primary coil (Vp) is also 26V.
Substituting the values into the formula:
(26V / 26V) = (Np / 100)
Simplifying the equation:
1 = (Np / 100)
Np = 100
Therefore, there are 100 turns in the primary coil.
b) To find the current in the primary coil, we can use the formula for power:
P = VI
Where:
P = Power (in watts)
V = Voltage (in volts)
I = Current (in amperes)
The power (P) is given as 54W, and the voltage in the primary coil (V) is 26V.
Substituting the values into the formula:
54W = (26V) * I
Solving for I:
I = 54W / 26V
I ≈ 2.08 A
Therefore, the current in the primary coil is approximately 2.08 A.