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

1 Answer

In a series RL (Resistor-Inductor) circuit, the relationship between current and voltage is characterized by the behavior of the inductor and the resistor when connected in series. The behavior of these elements depends on the rate of change of the current (di/dt) flowing through the inductor and the resistance of the resistor.

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.
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