Final answer:
The mutual inductance and the coefficient of coupling between two coils with self-inductances of 25mH and 55mH connected in series can be determined using formulas based on their total inductance of 0.1H.
Step-by-step explanation:
When two coils with self-inductances of 25mH and 55mH are connected in series and the total inductance is 0.1H, we can determine (a) the mutual inductance between the two coils and (b) the coefficient of coupling by applying the formula for the total inductance of two coils in series when they have mutual inductance. The formula is L_{total} = L_1 + L_2 ± 2M where L_1 and L_2 are the self-inductances of the two coils and M is the mutual inductance. In such a situation, we find M using the equation 0.1H = 0.025H + 0.055H ± 2M to solve for M. The positive or negative sign in front of 2M depends on whether the mutual inductance is aiding or opposing the field.
Next, the coefficient of coupling, denoted by k, is defined as the ratio of the mutual inductance M to the geometric mean of the individual self-inductances. The formula is k = M / √(L_1 × L_2). From the values given, one can calculate the coefficient of coupling. Remember, the value of k falls within the range of 0 to 1, where 1 indicates perfect coupling and 0 indicates no coupling.