Question 22.1: For the transformer in Fig. 22.3: a. Find the mutual inducta...
For the transformer in Fig. 22.3:
a. Find the mutual inductance M.
b. Find the induced voltage e_{p} \text { if the flux } \phi_{p} changes at the rate of 450 mWb/s.
c. Find the induced voltage e_{s} for the same rate of change indicated in part (b).
d. Find the induced voltages e_{p} \text { and } e_{s} \text { if the current } i_{p} changes at the rate of 0.2 A/ms.
\text { a. } M=k \sqrt{L_{p} L_{s}}=0.6 \sqrt{(200 mH )(800 mH )}.
=0.6 \sqrt{16 \times 10^{-2}}=(0.6)\left(400 \times 10^{-3}\right)=240 mH.
\text { b. } e_{p}=N_{p} \frac{d \phi_{p}}{d t}=(50)(450 mWb / s )=22.5 V.
\text { c. } e_{s}=k N_{s} \frac{d \phi_{p}}{d t}=(0.6)(100)(450 mWb / s )=27 V.
\text { d. } e_{p}=L_{p} \frac{d i_{p}}{d t}=(200 mH )(0.2 A / ms ).
=(200 mH )(200 A / s )= 4 0 V.
e_{s}=M \frac{d i_{p}}{d t}=(240 mH )(200 A / s )=48 V.