Question

1. the total inductance of parallel inductors is

a greater than the smallest inductance value
b greater than the largest inductance value
c less than the smallest inductance value
d less than the largest inductance value

Explanation:

The formula for the total inductance \(L_{total}\) of parallel inductors \(L_1,L_2,\cdots,L_n\) is \(\frac{1}{L_{total}}=\frac{1}{L_1}+\frac{1}{L_2}+\cdots+\frac{1}{L_n}\). For example, if we have two inductors \(L_1\) and \(L_2\) in parallel, \(L_{total}=\frac{L_1L_2}{L_1 + L_2}\). Suppose \(L_1=1H\) and \(L_2 = 2H\), then \(L_{total}=\frac{1\times2}{1 + 2}=\frac{2}{3}H\approx0.67H\). Here, the smallest inductance is \(1H\), and \(L_{total}<1H\). In general, for \(n\) inductors in parallel (\(n\geq2\)), since \(\frac{1}{L_{total}}>\frac{1}{L_{min}}\) (where \(L_{min}\) is the smallest inductance value among the parallel - connected inductors), then \(L_{total}

Answer:

C. less than the smallest inductance value