You probably want something like this.
When input is low, pullup will keep second transistor active. When signal gets high, first transistor will conduct and "connect" second one to ground thus turning it off.







simulate this circuit &ndash; Schematic created using CircuitLab

Make NPN transistor ground when low, 5V when high
I have a homework problem that was solved by our instructor: 

"Calculate the electric current of the inductor at \$t=0^+\$."



He calculated \$1/30\$ but the answer sheet was says \$-1/30\$.

Which of them is correct? 

Our instructor's work:






