[en] We analyze the properties of steady and time-dependent C shocks under conditions prevailing in giant molecular clouds. For steady C shocks, we show that ionization equilibrium holds and uses numerical integration to obtain a fitting formula for the shock thickness mediated by ambipolar diffusion, L_shock∝n₀^–3/4 v₀^1/2 B₀^1/2χ_i0^–1. Our formula also agrees with an analytic estimate based on ion-neutral momentum exchange. Using time-dependent numerical simulations, we show that C shocks have a transient stage when the neutrals are compressed much more strongly than the magnetic field. The transient stage has a duration set by the neutral-ion collision time, t_AD ∼ L_shock/v_drift ∼ 0.1-1 Myr. This transient creates a strong enhancement in the mass-to-magnetic flux ratio. Under favorable conditions, supercritical prestellar cores may form and collapse promptly as a result of magnetic flux loss during the transient stage of C shocks.