Question

What differential equation follows when \[v=v_m\sin\omega t\] is applied across a pure inductor?

Options

• \[\frac{di}{dt}=\frac{v_m}{L}\sin\omega t\]

• \[\frac{di}{dt}=\frac{v_m}{L}\cos\omega t\]

• \[\frac{di}{dt}=v_mL\sin\omega t\]

• \[\frac{di}{dt}=\frac{L}{v_m}\sin\omega t\]

Answer 1

Substitute the applied voltage into \[L\frac{di}{dt}=v\]. Dividing by \[L\] gives \[\frac{di}{dt}=\frac{v_m}{L}\sin\omega t\].