Torque and Current
Torque is proportional to the product of armature current and the resultant flux density per pole.
T = K × f × Ia
where T is torque, K is some constant, f is the flux density, and Ia is the armature current.
In series wound motors, flux density approximates the square root of current, so torque becomes approximately proportional to the 1.5 power of torque.
T = K × Ia1.5±
where T is torque, K is some constant, and Ia is the armature current.
Speed, Voltage, and Induced Voltage
Resistance of the armature widings has only a minor effect on armature current. Current is mostly determined by the voltage induced in the windings by their movement through the field. This induced voltage, also called "back-emf" is opposite in polarity to the applied voltage, and serves to decrease the effective value of that voltage, and thereby decreases the current in the armature.
An increase in voltage will result in an increase in armature current, producing an increase in torque, and acceleration. As speed increases, induced voltage will increase, causing current and torque to decrease, until torque again equals the load or induced voltage equals the applied voltage.
A decrease in voltage will result in a decrease of armature current, and a decrease in torque, causing the motor to slow down. Induced voltage may momentarily be higher than the applied voltage, causing the motor to act as a generator. This is the essense of regenerative breaking.
Induced voltage is proportional to speed and field strength.
Eb = K × N × f
where Eb is induced voltage, K is some constant particular to that motor, N is the speed of the motor, and f is the field strength.
This can be solved for speed to get the "Speed Equation" for a motor:
N = K × Eb ÷ f
where N is rpm, K is some constant (the inverse of the K above), Eb is the induced voltage of the motor, and f is the flux density.
Note that speed is inversely proportional to field strength. That is to say, as field strength decreases, speed increases.