Question

The current i(t) in the circuit shown below is?

(a) i(t)=(Vm/(R-jωL))e^tjω

(b) i(t)=(Vm(R+jωL)) e^tjω

(c) i(t)=(Vm(R-jωL)) e^tjω

(d) i(t)=(Vm/(R+jωL)) e^tjω

The question was asked during an interview.

This interesting question is from Impedence Diagram in chapter Complex Impedence of Network Theory

Answer 1

Right choice is (d) i(t)=(Vm/(R+jωL)) e^tjω

To explain: i(t)=Im e^tjω. Vm e^tjω=RIm e^tjω+L   d/dt (Im e^tjω). Vme^tjω=RIm e^tjω+L Im(jω)e^tjω. Im = Vm/(R+jωL). i(t)=(Vm/(R+jωL)) e^tjω.