Topic: Network Theory
Two coupled coils have self inductances $L_{1}=10~mH$ and $L_{2}=20~mH$. The coefficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin(314 t) A is
- A. 3.14 cos (314t) V
- B. 3.33 sin(314t) V
- C. 6.66 cos(314t) V
- D. 6.28 cos(314t) V
Answer: C. 6.66 cos(314t) V
Explanation: $M=K\sqrt{L_{1}L_{2}} = 0.75\sqrt{10\times10^{-3}\times20\times10^{-3}}=0.0106$. $V_{2}=M\frac{di}{dt}=0.0106\times2\times314~cos(314~t) = 6.66~cos(314~t)V$.