Problem 4.105

An oscillating circuit consists of two coils connected in series whose inductances are \(L_{1}\) and \(L_{2},\) active resistances are \(R_{1}\) and \(R_{2}\), and mutual inductance is negligible. These coils are to be replaced by one, keeping the frequency and the quality factor of the circuit constant. Find the inductance and the active resistance of such a coil.