Final answer:
The induced emf in the second coil is calculated using Faraday's law of electromagnetic induction, resulting in an emf of -0.75 V when the current in the first coil changes by 3A over 0.02 seconds. Therefore, the correct option is A.
Step-by-step explanation:
The student's question involves calculating the induced emf in a coil due to the change in current on another coil which it is coupled with through mutual inductance.
According to Faraday's law of electromagnetic induction, the induced emf (ε) in a coil can be found using the formula ε = -M (dI/dt), where M is the mutual inductance, and dI/dt is the rate of change of current over time.
In this case, the mutual inductance is given as 5 mH (millihenrys), and the change in current is 3 A (amperes) over 0.02 s (seconds).
Plugging these values in, the induced emf is calculated as follows:
ε = -M (dI/dt) = -5 x 10^-3 H * (3 A / 0.02 s)
= -0.75 V
Hence, the induced emf in the second coil is -0.75 V, corresponding to option (a).