Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from \(0\) A to \(6\) A in the first \(10\ \mu\)s and then falls linearly from \(6\) A to \(0\) A in the next \(10\ \mu\)s of every switching cycle as shown. The load resistance \(R\) is \(10\ \Omega\) and the capacitance \(C\) is \(500\ \mu\)F.
Neglect the ripple in the output voltage. What is the input voltage \(V_{dc}\)?