Figure shows the combination of inductances and capacitances. Resonant frequency of the L - C circuit is

Step-by-step solution

Resonant frequency analysis The series combination of inductors L and 2L yields equivalent inductance L_ eq = L + 2L = 3L . The parallel combination of capacitors C and 2C gives equivalent capacitance C_ eq = C + 2C = 3C . The resonant frequency follows from f₀ = 1 2 L_ eq C_ eq . Substituting gives f₀ = 1 2 9LC = 1 6 LC . This corresponds to option D .