A series LCR circuit is required to have a resonant angular frequency of 1000 rad s ⁻¹ and a bandwidth of 40 rad s ⁻¹ . If the resistance of the circuit is 20 , what must be the values of its inductance and capacitance respectively?

Step-by-step solution

Given ₀ = 1000 rad s ⁻¹ , = 40 rad s ⁻¹ , and R = 20 . The bandwidth of a series LCR circuit is given by = R L . Substituting the given values: 40 = 20 L L = 20 40 = 0.5 H The resonant angular frequency is given by ₀ = 1 LC . Squaring both sides: ₀^2 = 1 LC Substituting the values of ₀ and L : (1000)^2 = 1 0.5 C 10^6 = 2 C C = 2 10⁻⁶ F = 2 F Therefore, the inductance is 0.5 H and the capacitance is 2 F . Answer: 0.5 H and 2 F