The condition Q ( t ) = Q ( t 0 ) ∀ ∀ t > t 0 , corresponds to the absence of charge quantity change in the control volume: the system has reached a steady state. From the above condition, the following must hold true: ∫ ∫ t 0 t ( Q ˙ ˙ I N ( τ τ ) − − Q ˙ ˙ O U T ( τ τ ) ) d τ τ = 0 ∀ ∀ t > t 0 ⟹ ⟹ Q ˙ ˙ I N ( t ) = Q ˙ ˙ O U T ( t ) ∀ ∀ t > t 0 therefore, Q ˙ ˙ I N and Q ˙ ˙ O U T are equal (not necessarily constant) over time, then the overall charge inside the control volume does not change. This deduction could be derived directly from the continuity equation, since at steady state ∂ ∂ Q / ∂ ∂ t = 0 holds, and implies Q ˙ ˙ I N ( t ) = Q ˙ ˙ O U T ( t ) .