1. derivation of rc filtering properties consider an rc low-pass filter. a. using the relation i = c dv dt for a capacitor and ohm’s law v = ir for a resistor, show that the governing equation across the capacitor is given by vout + τ dvout dt = vin where τ = rc. b. suppose that the input and output voltages are varying sinusoidally, vin/out ∼ sin(ωt). since sin(ωt) = im(e iωt ), one can analyze the behavior using complex numbers. using variables vin = aine iωt , vo