Resonance and the laboratory work

If in a series R–L–C circuit the external voltage frequency makes X_L = X_C, the net reactance is zero and the impedance drops to its smallest value, Z = R. The current amplitude is then greatest, Iₘ = Uₘ/R: this is resonance in an electric circuit. From ωL = 1/(ωC) the resonance frequency is ω_res = 1/√(LC) (ν_res = 1/(2π√(LC))), i.e. the external frequency equals the natural frequency ω₀ of the circuit. The graph of current amplitude versus frequency is the resonance curve; the smaller R, the higher and narrower the peak. At resonance the voltages across the coil and capacitor are equal: U_L = U_C = Iₘ·X_L = (Uₘ/R)·√(L/C); if (1/R)√(L/C) > 1 they exceed the source voltage (hence the name voltage resonance) and can break down the insulation. In a radio receiver the circuit's capacitance or inductance is varied to make its natural frequency equal to that of the wanted station: the circuit resonates with that signal, which then stands out above the others.