Discuss the charging and discharging of a capacitor through a resistance?

Question: Discuss the charging and discharging of a capacitor through a resistance?

A capacitor is a device that can store electric charge by creating an electric field between two conductive plates. When a capacitor is connected to a battery through a resistor, it starts to charge up until the voltage across the capacitor is equal to the battery voltage. This process is called charging of a capacitor through a resistor.

The charging of a capacitor through a resistor can be described by the following equation:

Q = CV(1 - e^(-t/RC))

where Q is the charge on the capacitor, C is the capacitance, V is the battery voltage, R is the resistance, and t is the time.

The equation shows that the charge on the capacitor increases exponentially with time and approaches CV as t approaches infinity. The time constant RC determines how fast the capacitor charges up. The smaller the RC, the faster the capacitor charges up.

When a charged capacitor is disconnected from the battery and connected to a resistor, it starts to lose its charge by transferring current through the resistor. This process is called discharging of a capacitor through a resistor.

The discharging of a capacitor through a resistor can be described by the following equation:

Q = CVe^(-t/RC)

where Q is the charge on the capacitor, C is the capacitance, V is the initial voltage across the capacitor, R is the resistance, and t is the time.

The equation shows that the charge on the capacitor decreases exponentially with time and approaches zero as t approaches infinity. The time constant RC determines how fast the capacitor discharges. The larger the RC, the slower the capacitor discharges.

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