Almost every circuit I have seen as an rf receiver, it uses inductor and a capacitor as a tank circuit. Why not just use RC circuit with opamps to select a specific frequency and than get desired gain too?
first, op amps don't work well at RF frequencies. Those that do are expensive. second, a frequency filter using only R's and C's has a pretty broad bandwidth, and would not select adjacent channels very well.
You need a sensing resistor only when measuring current. If you want capacitor current, the resistor is put in series with the capacitor and similarly for inductor current.
Because in an LC circuit, the L (inductor) has a cutoff frequency that allows lower frequencies to pass (low pass), while the C (capacitor) allows more to pass (high pass) as the frequency goes higher. Together they select a frequency to pass (band pass.) in an RC circuit it will pass more of the frequency as it gets higher, as it's only a high pass and can't be a frequency selector.
