What value of inductor should be connected in parallel with a series combination of 4 H and 2 H so that the effective inductance of the circuit is 3 H?
6 H
First combine the two series inductors: \(L_{s}=4+2=6\ \text{H}\).
Let the unknown parallel inductor be \(L\). For two inductors in parallel the effective value is \(L_{eff}=\dfrac{L_{s}L}{L_{s}+L}=\dfrac{6L}{6+L}\).
Set this equal to 3 H: \(\dfrac{6L}{6+L}=3\).
Cross-multiply: \(6L=3(6+L)=18+3L\), so \(3L=18\) and \(L=6\ \text{H}\).
Hence, a 6 H inductor must be connected in parallel.
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