The PHIBEX (Physics Ignition and Burn Experiment) tokamaks are small (R-0.57 m, a-0.22 m), inexpensive, modular, high field, OH and D-T alpha heated machines designed to demonstrate ignition and thermonuclear burn. Ohmic Heating (OH) bias current minimization is critical due to the small allowable size of the central OH coil and the high material stresses. Water cooled copper OH and Vertical Field (VF) coils are considered, as well as conducting and nonconducting first walls. The coupled equations for the OH, VF, plasma, and wall circuits are solved with the plasma current (3.3 MA peak), plasma resistance, and poloidal beta Bp (3.3 peak) as driving functions. The system inductances are calculated with the UT-CEM tokamak inductance code TINDERS. The wall de resistance is derived. The VF and plasma currents are related by finite element magnetic code analysis and Bp in the plasma inductance express ion. OH bias currents (33-39 kA) are determined for several coil configurations and plasma current variations which extend into the burn period. Required OH and VF power supply voltages, currents, powers, and energies are calculated as are coil dissipations. The effects of conducting first walls without flux breaking insulating slits are investigated. Wall currents (to 250 kA), resistive volt-sec, dissipated powers, and temperature rises (to 23 c) are obtained for several wall resistances. Four designs with nonconducting walls are compared.