Question

1. the total inductance in this circuit is________. a 18 mh b 9 mh c 4 mh d 2 mh

Explanation:

Step1: Identify the connection type

The inductors \(L_1 = 3\space mH\) and \(L_2=6\space mH\) are in parallel.

Step2: Use the formula for parallel inductors

The formula for the total inductance \(L_{total}\) of two inductors \(L_1\) and \(L_2\) in parallel is \(\frac{1}{L_{total}}=\frac{1}{L_1}+\frac{1}{L_2}\).
Substitute \(L_1 = 3\space mH\) and \(L_2 = 6\space mH\) into the formula:
\(\frac{1}{L_{total}}=\frac{1}{3}+\frac{1}{6}\).
Find a common denominator (6): \(\frac{1}{L_{total}}=\frac{2 + 1}{6}=\frac{3}{6}=\frac{1}{2}\).
Take the reciprocal of both sides: \(L_{total}=2\space mH\).

Answer:

d. \(2\space mH\)