Graphs of Charge and Discharge

Introduction

• Capacitors exhibit specific charge and discharge behaviours that are represented by exponential curves in graphs.
• Understanding these graphs is crucial for analysing capacitor circuits and their time-dependent characteristics.

Charge and Discharge Curves

• Capacitor charge and discharge graphs display the relationship between voltage, current, and time.
• During charging, the voltage across the capacitor increases gradually, and the current decreases over time.
• During discharging, the voltage decreases gradually, and the current increases over time.
• These curves are characterised by exponential changes.

Charging Graph

• In the charging graph, the voltage increases as the capacitor charges, approaching the supply voltage (E).
• The current (I) decreases during charging as the capacitor stores more charge.
• Mathematically, during charging: I = E/R, where R is the resistance in the circuit.
• The charging process is gradual, and the curve represents the approach to full charge.

Discharging Graph

• In the discharging graph, the voltage decreases as the capacitor discharges, eventually reaching zero.
• The current (I) increases during discharging as the stored charge is released.
• Mathematically, during discharging: I = -E/R, where R is the resistance in the circuit.
• The discharging process is gradual, and the curve represents the release of stored charge.

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Graphs of Charge and Discharge

Effect of Capacitance and Resistance

• The values of capacitance (C) and resistance (R) in a circuit significantly impact the charge and discharge curves.
• Larger capacitance results in longer charge and discharge times because the capacitor can store more charge.
• Larger resistance leads to longer charge and discharge times as it limits the flow of current.

Summary

• Capacitor charge and discharge graphs exhibit exponential curves.
• Charging curves show voltage increasing and current decreasing.
• Discharging curves show voltage decreasing and current increasing.
• Capacitance and resistance values in the circuit affect the time it takes for charging and discharging.
• Understanding these graphs helps in analysing the behaviour of capacitor circuits.
• Electrons do not cross the gap in the capacitor during charging; instead, electron flow is absorbed and provided by the plates.