Growth and Decay of Current in LR and RC Circuits Learning Objectives: Define the terms growth and decay in an LR and RC circuit. Explain the relati...
Growth and Decay of Current in LR and RC Circuits
Learning Objectives:
Define the terms growth and decay in an LR and RC circuit.
Explain the relationship between resistance, inductance, and current.
Describe how the growth and decay of current differ in LR and RC circuits.
Introduction:
In an LR circuit (Inductive Reactance Circuit), there is a relationship between the applied voltage, resistance, and inductance. The current in an LR circuit grows or decays with time, depending on the properties of the circuit. Conversely, in an RC circuit (Capacitive Reactance Circuit), the current either grows or decays with time, depending on the properties of the circuit.
LR Circuit:
In an LR circuit, the current growth or decay is determined by the product of the resistance and the inductance. The general formula for the current in an LR circuit is:
I = E / (R + iL)
where:
I is the current in amperes
E is the applied voltage in volts
R is the resistance in ohms
i is the reactance in ohms
L is the inductance in henrys
When R >> L:
When the resistance is much greater than the inductance, the current in an LR circuit will decay exponentially with time.
This is because the inductance effectively blocks the flow of current, preventing the current from growing.
When R << L:
When the resistance is much less than the inductance, the current in an LR circuit will grow exponentially with time.
This is because the inductance allows a significant amount of current to flow through it, resulting in a high current.
RC Circuit:
In an RC circuit, the current growth or decay is determined by the product of the resistance and the capacitance. The general formula for the current in an RC circuit is:
I = E / (R + 1/iC)
where:
I is the current in amperes
E is the applied voltage in volts
R is the resistance in ohms
i is the reactance in ohms
C is the capacitance in farads
When R >> C:
When the resistance is much greater than the capacitance, the current in an RC circuit will also decay exponentially with time.
This is because the capacitance effectively blocks the flow of current, preventing the current from growing.
When R << C:
When the resistance is much less than the capacitance, the current in an RC circuit will grow exponentially with time.
This is because the capacitance allows a significant amount of current to flow through it, resulting in a high current.
Conclusion:
In summary, the growth and decay of current in an LR circuit are determined by the product of resistance and inductance, while the growth and decay of current in an RC circuit are determined by the product of resistance and capacitance