Consider a source of voltage \(v(t)=10 \sqrt{2} \sin (2 t) \mathrm{V}\), with an internal resistance of \(1800 \Omega\). A transformer that can be considered as ideal is used to couple a \(50-\Omega\) resistive load to the source.

(a) Determine the transformer primary-to-secondary turns ratio required to ensure maximum power transfer by matching the load and source resistances.

(b) Find the average power delivered to the load, assuming maximum power transfer.