For a first order lowpass filter with unity $\text {d.c}$. gain and $-3\;\text {dB}$ corner frequency of $2000\pi \:\text {rad/s}$,the transfer function $H(j\omega)$ is
- $\frac{1}{1000+j\omega}$
- $\frac{1}{1+j1000\omega}$
- $\frac{2000\pi}{2000\pi+j\omega}$
- $\frac{1000\omega}{1+j1000\omega}$