Electrostatics - Transient Relations During Charging/Discharging of Capacitor
1 Answer
During the charging and discharging of a capacitor in an electrical circuit, several transient relationships describe the behavior of key parameters. Let's discuss these relations:
Charging of a Capacitor:
When a previously uncharged capacitor is connected to a voltage source (e.g., a battery) through a resistor, it starts to charge. The voltage across the capacitor (Vc) and the current through the resistor (I) change over time.
Voltage across the Capacitor (Vc): The voltage across the capacitor as a function of time during charging is given by the formula:
Where:
Vc is the voltage across the capacitor at time t.
V is the final voltage (voltage of the source).
t is time.
R is the resistance in the circuit.
C is the capacitance of the capacitor.
Current through the Resistor (I): The current through the resistor as a function of time during charging is given by:
Where:
I is the current through the resistor at time t.
Discharging of a Capacitor:
When a charged capacitor is disconnected from a voltage source and connected to a resistor, it starts to discharge. The voltage across the capacitor and the current through the resistor change over time.
Voltage across the Capacitor (Vc): The voltage across the capacitor as a function of time during discharging is given by:
Where:
Vc is the voltage across the capacitor at time t.
Current through the Resistor (I): The current through the resistor as a function of time during discharging is given by:
Where:
I is the current through the resistor at time t.
These equations describe the transient behaviors of a charging and discharging capacitor in an RC (resistor-capacitor) circuit. The time constant, τ (tau), of the circuit is defined as τ = R * C. It represents the time it takes for the voltage or current to change to approximately 63.2% of its final value during charging or discharging. The smaller the time constant, the faster the capacitor charges or discharges.
Charging of a Capacitor:
When a previously uncharged capacitor is connected to a voltage source (e.g., a battery) through a resistor, it starts to charge. The voltage across the capacitor (Vc) and the current through the resistor (I) change over time.
Voltage across the Capacitor (Vc): The voltage across the capacitor as a function of time during charging is given by the formula:
Where:
Vc is the voltage across the capacitor at time t.
V is the final voltage (voltage of the source).
t is time.
R is the resistance in the circuit.
C is the capacitance of the capacitor.
Current through the Resistor (I): The current through the resistor as a function of time during charging is given by:
Where:
I is the current through the resistor at time t.
Discharging of a Capacitor:
When a charged capacitor is disconnected from a voltage source and connected to a resistor, it starts to discharge. The voltage across the capacitor and the current through the resistor change over time.
Voltage across the Capacitor (Vc): The voltage across the capacitor as a function of time during discharging is given by:
Where:
Vc is the voltage across the capacitor at time t.
Current through the Resistor (I): The current through the resistor as a function of time during discharging is given by:
Where:
I is the current through the resistor at time t.
These equations describe the transient behaviors of a charging and discharging capacitor in an RC (resistor-capacitor) circuit. The time constant, τ (tau), of the circuit is defined as τ = R * C. It represents the time it takes for the voltage or current to change to approximately 63.2% of its final value during charging or discharging. The smaller the time constant, the faster the capacitor charges or discharges.