Mutual Induction — Question 4

Question 4

Series aiding and opposing measurements reveal coupling strength

Two fixed coils have L1=4.00 mH and L2=9.00 mH. Their measured series inductances are 22.6 mH for aiding connection and 3.40 mH for opposing connection. Use positive M.

1. Infer mutual inductance from the two series measurements.

2. Find coupling coefficient $k=M/\sqrt{L_1L_2}$ and check the measured sum.

Question 4 - Solution

Series aiding and opposing measurements reveal coupling strength

(a) Method and calculation

$$L_a=L_1+L_2+2M,\quad L_o=L_1+L_2-2M.$$$$\boxed{M=(L_a-L_o)/4=4.80\,mH}.$$

(b) Interpretation and further calculation

$$\boxed{k=4.80/\sqrt{(4.00)(9.00)}=.800}.$$$$\boxed{L_a+L_o=26.0\,mH=2(L_1+L_2)}.$$

Physical check

Changing the series connection reverses the mutual term while leaving the two self-inductances unchanged.