"Modern energy for all," an internationally supported initiative to connect populations to electricity services, is expected to help reduce poverty-induced vulnerabilities. It has become a primary strategy for meeting sustainable development goals, especially in sub-Saharan Africa. However, when electricity is supplied by a capacity-constrained grid to a resource-constrained population, the service quality can vary both spatially and temporally. This research explores the quality of electricity services based on a case study of Unguja, Tanzania. Using 1) open-ended interviews, 2) detailed electricity-systems monitoring, and 3) household surveys, we show how voltage quality varies significantly, even within highly localized settings. Fluctuations result in dim lights at best and power outages and broken appliances at worst, denying many Unguja residents the expected benefits of access to modern energy. By combining an extensive understanding of the physical system together with interviews and surveys, this work presents a unique mapping of voltage quality in a system that is financially and physically constrained and highlights the consequences of poor-quality service for poor users.