The charge flowing through a resistance \(R\) is given by,
        \(q = A\sin\omega t+B\cos\omega t\)
The heat produced in the resistance over a very long time \(\Delta t\) (much greater than \(T = 2\pi/ \omega\)) is:
1. \(\omega^{2}\left(A^{2}+B^{2}\right) R \Delta t\)
2. \(\omega^{2}\left(A^{2}-B^{2}\right) R \Delta t\)
3. \(\dfrac{1}{2} \omega^{2}\left(A^{2}+B^{2}\right) R \Delta t\)
4. \(\dfrac{1}{2} \omega^{2}\left(A^{2}-B^{2}\right) R \Delta t\)