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When dealing with electrical circuits, understanding equivalence is crucial. The equivalent inductance of a system simplifies complex networks of inductors into a single inductor that has the same magnetic and electrical properties as the system it represents. In a parallel configuration, the total magnetic effect is distributed across several inductors.To find the equivalent inductance for inductors in parallel, like in the given problem, we use a formula similar to calculating resistors in parallel, just reversed. For two inductors with inductances \(L_1\) and \(L_2\), their total or equivalent inductance \(L_t\) is found using:\[ \frac{1}{L_t} = \frac{1}{L_1} + \frac{1}{L_2} \]This formula allows for the calculation of a single inductance value that represents the combined effect of the two parallel inductors. This calculation is essential in designing circuits and ensuring energy efficiency. Once we understand how to calculate the equivalent inductance, we can simplify complex circuit analyses.

Calculating inductance, especially for parallel inductors, is crucial in electrical engineering and physics. In this scenario, we substitute known values of \(L_1 = 0.030 \mathrm{H}\) and \(L_2 = 0.060 \mathrm{H}\) into the formula for parallel inductance:\[ \frac{1}{L_t} = \frac{1}{0.030} + \frac{1}{0.060} \]Breaking it down:- Convert each inductance value into its reciprocal: - \( \frac{1}{0.030} = 33.33 \) - \( \frac{1}{0.060} = 16.67 \)- Add these reciprocals to find the total: \[ 33.33 + 16.67 = 50.00 \] Finally, find the reciprocal of the sum to determine the equivalent inductance:\[ L_t = \frac{1}{50.00} \approx 0.020 \mathrm{H} \]This process highlights the core principles of solving parallel inductor problems, where effectively handling the reciprocals is key.

Approaching a physics problem step-by-step ensures clarity and accuracy. The approach taken in the solution simplifies a potentially complex topic into manageable steps.

• Step 1 involved understanding what the problem is asking, which is crucial for finding the right path forward.
• Step 2 introduced the necessary formula, which serves as the mathematical foundation for solving the problem.
• Step 3 to Step 5 encompassed the substitution of known values and calculation of results, which translates theory into practical application.
• Finally, Step 6 concluded by delivering the final answer, tying the solution back to the physical scenario.

Such a structured method not only resolves this particular problem but builds a useful analytical procedure for approaching various physics exercises. These steps embody a logical pathway that helps ensure that nothing is missed and each part of the problem is addressed systematically. This methodical breakdown into easily digestible parts encourages a deeper understanding and solid foundation for solving more advanced physics problems.