How to Calculate Equivalent Resistance in AC Coupled Circuits

TL;DR

To calculate the equivalent resistance of inductors in parallel with mutual coupling, use the cumulative coupling formula: L1 * L2 - M² / (L1 + L2 - 2M) and the differential coupling formula: L1 - M² / (L1 + L2 + 2M). Ensure units are consistent for accurate results.

Transcript

in this case uh you'll be having two coins with self-inductance l1 and l2 are connected in parallel if the mutual coupling between them is 5 that means m is equal to 5 since if you know carefully all the values are milli so we don't need to always put the value into 10 plus minus 3 all the values are mini if we calculate that a particular term but ... Read More

Key Insights

• 🖐️ Self-inductance and mutual coupling play important roles in determining the behavior of inductors in electrical circuits.
• ❓ The equivalent resistance of inductors connected in parallel can be calculated using different coupling formulas.
• 🇦🇪 Paying attention to units and using shortcuts for calculations can simplify the analysis of inductors in circuits.

Questions & Answers

Q: What is the purpose of self-inductance in an electrical circuit?

Self-inductance is a property of an inductor that resists changes in the current flowing through it, creating a magnetic field that stores energy.

Q: What is mutual coupling between inductors?

Mutual coupling refers to the influence of one inductor's magnetic field on another inductor in close proximity, affecting their inductance values.

Q: How is the equivalent resistance calculated for inductors connected in parallel?

The cumulative coupling formula is used, which takes into account the self-inductance, mutual coupling, and the individual inductance values of the inductors.

Q: What is the difference between cumulative and differential coupling formulas?

The only difference is in the denominator of the formulas. The cumulative formula has -2M, while the differential formula has +2M.

Summary & Key Takeaways

• Two coins with self-inductance L1 and L2 are connected in parallel with mutual coupling M = 5.

• To find the equivalent resistance, the cumulative and differential coupling formulas are used.

• The cumulative coupling formula is L1 L2 - M^2 / (L1 + L2 - 2M), while the differential coupling formula is L1 - M^2 / (L1 + L2 + 2M).