RL circuits combine resistors and inductors, creating unique electrical behavior. When voltage is applied, current doesn't instantly reach its maximum. Instead, it grows exponentially, governed by the . This gradual change is due to the 's opposition to current changes.
The circuit's response depends on the balance between and . A larger or smaller resistor slows current changes, while the opposite speeds them up. Energy is stored in the inductor's , affecting how the circuit charges and discharges over time.
RL Circuits
Behavior in RL circuits
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Reactance, Inductive and Capacitive · Physics View original
Connecting a voltage source to an RL circuit causes current to begin flowing
Current increases exponentially over time, approaching a maximum value of Imax=RV
The rate of current increase is determined by the inductive τ=RL
The current equation during charging is I(t)=RV(1−e−τt)
an RL circuit
Removing the voltage source and shorting the circuit causes current to begin decreasing
Current decreases exponentially over time, approaching zero (exhibiting )
The rate of current decrease is determined by the inductive time constant τ=RL
The current equation during discharging is I(t)=I0e−τt, where I0 is the initial current
Voltage across the resistor
During charging, the voltage across the resistor is [VR(t)](https://www.fiveableKeyTerm:VR(t))=RI(t)=V(1−e−τt)
During discharging, the voltage across the resistor is VR(t)=RI(t)=RI0e−τt
Voltage across the inductor
During charging, the voltage across the inductor is [VL(t)](https://www.fiveableKeyTerm:VL(t))=LdtdI=Ve−τt
During discharging, the voltage across the inductor is VL(t)=LdtdI=−RI0e−τt
Kirchhoff's voltage law applies to RL circuits, stating that the sum of voltages around any closed loop in the circuit must equal zero
Inductive time constant effects
The inductive time constant τ=RL determines the rate of current change in an RL circuit
A larger time constant results in a slower rate of current change (larger inductor or smaller resistor)
A smaller time constant results in a faster rate of current change (smaller inductor or larger resistor)
The time constant represents the time required for the current to reach approximately 63.2% of its final value during charging or to decrease to approximately 36.8% of its initial value during discharging
After one time constant, the current in an RL circuit reaches I(t)=Imax(1−e−1)≈0.632Imax during charging
After one time constant, the current in an RL circuit decreases to I(t)=I0e−1≈0.368I0 during discharging
The inductor opposes changes in current, causing the gradual increase or decrease in current over time due to its stored magnetic energy
Energy in inductor's magnetic field
The energy stored in the magnetic field of an inductor is given by E=21LI2
L is the inductance in henries (H)
I is the current flowing through the inductor in amperes (A)
The energy is stored in the magnetic field surrounding the inductor when current flows through it
As the current increases during charging, the energy stored in the magnetic field increases
As the current decreases during discharging, the energy stored in the magnetic field decreases
The maximum energy stored in the inductor occurs when the current reaches its maximum value Imax=RV, resulting in Emax=21LImax2=21L(RV)2
The stored energy in the inductor's magnetic field can be released back into the circuit during discharging, causing the current to decrease gradually instead of instantaneously
Power and Phase in RL Circuits
in an RL circuit occurs primarily in the resistor, converting electrical energy to heat
The in an RL circuit represents the time delay between the voltage and current waveforms
In AC circuits, the inductor causes the current to lag behind the voltage by a determined by the circuit's characteristics