What is the inductance of a coil if the coil produces an emf of 8.20 V when the current in it changes from -28.0 mA to +31.0 mA in 45.5 ms?
To calculate the inductance of a coil using known values of emf, current change, and time, you can use Faraday's Law of electromagnetic induction.
Faraday's Law states that the induced electromotive force (emf), in volts, is equal to the negative of the rate of change of magnetic flux through a coil. Mathematically, it can be written as:
emf = -dΦ/dt
Where:
- emf is the induced electromotive force (in volts),
- dΦ/dt is the rate of change of magnetic flux (in webers per second or Tesla-meter² per second).
In terms of inductance, the rate of change of current (di/dt) is related to the rate of change of magnetic flux (dΦ/dt) by the equation:
di/dt = -(emf / L)
Where:
- di/dt is the rate of change of current (in amperes per second),
- L is the inductance of the coil (in henries).
To calculate the inductance, rearrange the equation to solve for L:
L = -(emf / (di/dt))
Given Values:
- emf = 8.20 V
- Initial current (i1) = -28.0 mA = -0.028 A
- Final current (i2) = +31.0 mA = +0.031 A
- Time (dt) = 45.5 ms = 45.5 × 10⁻³ s
First, calculate the rate of change of current (di/dt):
di/dt = (i2 - i1) / dt
Substitute the known values and calculate di/dt.
di/dt = (+0.031 A - (-0.028 A)) / (45.5 × 10⁻³ s)
Now, substitute the calculated di/dt and the known emf into the rearranged equation to find the inductance (L):
L = -(emf / di/dt)
Substitute the known values and calculate L.