Calculate the equivalent inductance of multiple inductors connected in parallel.
When inductors are connected in parallel, the reciprocal of the total inductance is the sum of the reciprocals of the individual inductances.
This formula is only valid if there is no mutual inductance between the inductors. The equivalent inductance is always smaller than the smallest individual inductor.
For two inductors: L_eq = (L₁ * L₂) / (L₁ + L₂)
Given:
Step 1: Calculate Reciprocal Sum
Step 2: Calculate Equivalent Inductance
Result: Three inductors (10H, 20H, 15H) in parallel have an equivalent inductance of 4.61 H, which is much smaller than the smallest individual inductor (10H).
Why is parallel inductance smaller than series inductance?
In parallel, multiple paths exist for current flow, and each inductor only needs to handle part of the total current. The combined opposition to current change is less than any single inductor alone.
How do I calculate equivalent inductance for two parallel inductors?
For exactly two inductors, use the simplified formula: L_eq = (L₁ × L₂) / (L₁ + L₂). For three or more, use the reciprocal formula: 1/L_eq = 1/L₁ + 1/L₂ + ...
What if parallel inductors have different values?
The formula works regardless of whether inductors are equal or different. Unequal values are common in practice and simply follow the same reciprocal calculation.
Is equivalent inductance always less than the smallest inductor?
Yes, in parallel, the equivalent inductance is always smaller than the smallest individual inductor value. This is opposite to resistors in parallel, where R_eq is also smaller.
When would I use parallel inductors?
Parallel inductors reduce equivalent inductance for applications needing lower impedance, improve current sharing in high-current circuits, or provide redundancy if one component fails.
Does mutual inductance affect parallel inductance calculation?
Yes, mutual inductance between closely spaced parallel inductors can significantly alter the result. The reciprocal formula assumes no magnetic coupling between inductors.
What's the current distribution in parallel inductors?
In ideal parallel inductors, voltage across all branches is equal. Initial current distribution depends on inductor values and the rate of voltage change (dV/dt).
What happens at DC with parallel inductors?
At DC, inductors act as shorts (zero resistance). All inductors appear in parallel as resistances. DC current distribution depends only on the resistance of the inductor wire.
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