Equilibrium thermal noise is known to destroy any quantum phase transition. What are the effects of non-equilibrium noise? In two recent papers, we have considered the specific case of a resistively shunted Josephson junction driven by 1/f charge noise. At equilibrium, this system undergoes a sharp quantum phase transition at a critical value of the shunt resistance. By applying a real-time renormalization group approach, we found that the noise has three main effects: it shifts the phase transition, renormalizes the resistance and generates an effective temperature. In this paper, we explain how to understand these effects using simpler arguments based on Kirchhoff laws and time-dependent perturbation theory. We also show how these effects modify physical observables and especially the current–voltage characteristic of the junction. In the appendix, we describe two possible realizations of the model with ultracold atoms confined to one dimension.