You have a coil with 20 loops inside a magnetic field generator that is temporarily generating a field that has a rate of change of -0.25. The other end of this coil is wrapped around a core with 15 turns. How many turns must a second coil wrapped around the same coil have to produce an output voltage of 25 V?
To solve this problem, we need to use Faraday's law of electromagnetic induction, which states that the induced voltage in a coil is directly proportional to the rate of change of the magnetic field and the number of turns in the coil.
First, let's calculate the induced voltage in the first coil.
Given:
Number of loops in the first coil (N₁) = 20
Rate of change of the magnetic field (dΦ/dt) = -0.25
Using Faraday's law of electromagnetic induction:
Induced voltage (V₁) = -N₁ * dΦ/dt
Substituting the values:
V₁ = -20 * (-0.25)
V₁ = 5 V
Now, let's calculate the required number of turns (N₂) in the second coil to produce an output voltage of 25 V.
Given:
Output voltage (V₂) = 25 V
Using Faraday's law of electromagnetic induction:
V₂ = -N₂ * dΦ/dt
Solving for N₂:
N₂ = -V₂ / dΦ/dt
Substituting the values:
N₂ = -25 / (-0.25)
N₂ = 100 turns
So, the second coil must have 100 turns to produce an output voltage of 25 V.