Final answer:
To find the change in the primary current, we use the induced EMF in the secondary circuit calculated through Ohm's Law and the formula for induced EMF involving mutual inductance. The result is a change of 1.01475 A in the primary current during the 66-ms interval.
Step-by-step explanation:
To find the change in the primary current, we will use the concept of mutual inductance and Faraday's law of electromagnetic induction. When a change in the current in the primary coil occurs, it induces an electromotive force (EMF) in the secondary coil, which leads to a current in the secondary circuit. The induced EMF in the secondary coil (E) can be calculated using Ohm's Law, E = I2R, where I2 is the current in the secondary coil and R is the resistance of the secondary circuit. We are given that I2 = 4.1 mA (or 4.1 x 10-3 A) and R = 12Ω. Thus, E = (4.1 x 10-3 A)(12Ω) = 4.92 x 10-2 V. Next, we use the formula for the induced EMF due to mutual inductance, E = -M(dI1/dt), where M is the mutual inductance and dI1/dt is the rate of change of the current in the primary coil. We can rearrange this formula to solve for the rate of change of primary current, yielding dI1/dt = E/M. Substituting the given values, M = 3.2 mH (or 3.2 x 10-3 H) and the change in time dt = 66 ms (or 66 x 10-3 s), we have dI1/dt = (4.92 x 10-2 V) / (3.2 x 10-3 H) = 15.375 A/s. The total change in the primary current (∆I1) can then be calculated by multiplying this rate by the change in time, ∆I1 = (dI1/dt) × dt. Therefore, ∆I1 = (15.375 A/s)(66 x 10-3 s) = 1.01475 A, which is the change in the primary current during the 66-ms interval.