What is the relationship between the current and voltage in a series RL circuit?

Resistor (R):

The resistor obeys Ohm's law, which states that the voltage (V) across a resistor is directly proportional to the current (I) flowing through it. The relationship is given by:

V = I * R

Where:

V = Voltage across the resistor (in volts)

I = Current flowing through the resistor (in amperes)

R = Resistance of the resistor (in ohms)

Inductor (L):

The inductor opposes changes in the current flowing through it. When the current changes, the inductor induces an electromotive force (EMF) that creates a back-EMF to resist the change. The voltage across an inductor is given by:

V = L * (di/dt)

Where:

V = Voltage across the inductor (in volts)

L = Inductance of the inductor (in henrys)

di/dt = Rate of change of current (in amperes per second)

Combining both elements in a series RL circuit, the total voltage across the series combination is the sum of the voltage across the resistor and the voltage across the inductor:

Total Voltage (V_total) = V_resistor + V_inductor

V_total = I * R + L * (di/dt)

In summary, in a series RL circuit, the voltage-current relationship involves the resistor obeying Ohm's law, and the inductor opposing changes in current flow through the generation of back-EMF. The behavior of the circuit is determined by the interplay of these two elements when subjected to varying currents.