For the general time-dependent inductance-capacitance coupled circuits,quantumclassical correspondence and the quantum fluctuations are studied by using the Heisenberg correspondence principle. Through the wave functions and exact solution of equations of motion in Heisenberg picture,the classical solution is derived from quantum solution in the limit of large quantum numbers carrying out the average over the initial phase in the matrix elements,quantum fluctuations of the charges and magnetic fluxes are obtained. When the inductances in the circuit increase and the capacitances decrease exponentially with time,quantum fluctuations of the charge and current decrease exponentially with time;When the inductances and capacitances in the two component circuits are equal to each other and time-independent,it is found that the coupling capacitance tends to reduce the quantum fluctuations of the electric current and the coupling inductance tends to reduce the charge quantum fluctuations.