A voltage waveform v $=8$sin$(2000$t$)$V is input to a full$-$wave rectifier. A resistance of R $=50$k $$ is connected at the load. $[$ Assume that the diodes used in the circuit have a forward drop of $0\mathrm{.}8$ V$].$

$($a$)$ Draw the circuit of the full wave rectifier. Label the input and output voltages properly.

$($b$)$ Draw the waveforms of the input and output voltages. What are the peak values of input and output? Show them in the graph.

$($c$)$ Find the average voltage measured at the output.