This paper presents experimental and analytical studies on the characteristic resistance of NI (no-insulation) ReBCO pancake coils, which are used in an equivalent circuit model to characterize 'radial as well as spiral' current paths within the NI coils. We identified turn-to-turn contact resistance as a major source of the characteristic resistance of an NI coil. In order to verify this, three single pancake NI HTS coils-60, 40, 20 turns-were fabricated with their winding tension carefully maintained constant. A sudden discharge test was performed on each coil to obtain its characteristic resistance, and the relation between the turn-to-turn contact and the characteristic resistance was investigated. Based on the characteristic resistance and the n-value model, an equivalent circuit model was proposed to characterize the time-varying response of the NI coils. Charging tests were performed on the three test coils and the experimental results were compared with the simulated ones to validate the proposed approach with the equivalent circuit model.