If the current in a 100 mH coil changes steadily from 25.0 A to 10.0 A in 375 ms, what is the magnitude of the induced emf?
To find the magnitude of the induced emf, we can use Faraday's law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux through the coil.
The formula to calculate the induced emf is:
emf = -N * (dΦ/dt)
Where:
- emf is the induced electromotive force (emf) in volts (V)
- N is the number of turns in the coil
- dΦ/dt is the rate of change of magnetic flux through the coil in Weber per second (Wb/s)
In this case, we have:
- N = 1 (since there is only one coil)
- dΦ/dt = ΔΦ/Δt
To find the change in magnetic flux, we can use the formula:
ΔΦ = L * ΔI
Where:
- ΔΦ is the change in magnetic flux in Weber (Wb)
- L is the inductance of the coil in Henry (H)
- ΔI is the change in current in Amperes (A)
Given:
- L = 100 mH = 100 * 10^-3 H
- ΔI = 25.0 A - 10.0 A = 15.0 A
- Δt = 375 ms = 375 * 10^-3 s
Now, let's calculate the change in magnetic flux:
ΔΦ = L * ΔI
= (100 * 10^-3 H) * 15.0 A
= 1.5 Wb
Next, let's calculate the rate of change of magnetic flux:
dΦ/dt = ΔΦ/Δt
= 1.5 Wb / (375 * 10^-3 s)
= 4 Wb/s
Finally, let's calculate the induced emf using the formula:
emf = -N * (dΦ/dt)
= -(1) * (4 Wb/s)
= -4 V
So, the magnitude of the induced emf is 4 volts.