Answer:The mutual inductance (M) between the two coils is approximately -0.01125 V·s/A or -11.25 mH (millihenries).
Step-by-step explanation:
emf = -M * (dI/dt)
Where:
emf is the induced electromotive force,
M is the mutual inductance between the coils,
dI/dt is the rate of change of current in the first coil.
In this case, we are given that the current in one coil is switched off in 0.75 ms (or 0.75 × 10^(-3) seconds) and the induced average emf in the other coil is 11 V. The rate of change of current can be calculated by dividing the change in current by the time it takes:
dI/dt = ΔI / Δt
Since the current is switched off, ΔI is equal to the initial current, which is 4.5 A. The time interval is 0.75 ms.
ΔI = 4.5 A
Δt = 0.75 × 10^(-3) s
Now we can substitute these values into the equation for the induced emf:
11 V = -M * (4.5 A / (0.75 × 10^(-3) s))
Simplifying the equation:
M = -11 V * (0.75 × 10^(-3) s) / 4.5 A
M = -0.01125 V·s / A
The mutual inductance (M) between the two coils is approximately -0.01125 V·s/A or -11.25 mH (millihenries).