What happens in an RC circuit when the voltage is interrupted suddenly?

An RC circuit consists of a resistor (R) and a capacitor (C) connected in series or parallel. When a voltage is suddenly interrupted, there are two possible scenarios to consider:

Charging Phase (Initial condition: Capacitor uncharged):

If the capacitor was initially uncharged (no voltage across it), and the voltage source is suddenly connected to the circuit, the capacitor starts charging.

As the capacitor charges up, it builds up an electric field across its plates, and the voltage across the capacitor gradually increases over time.

The rate at which the capacitor charges depends on the time constant of the circuit, given by the product of the resistance (R) and the capacitance (C) (ฯ = R * C). The time constant represents the time it takes for the capacitor to reach approximately 63.2% of its final voltage.

When the voltage source is suddenly interrupted in this charging phase, the capacitor will discharge through the resistor, gradually decreasing the voltage across the capacitor over time. The time it takes for the capacitor to discharge significantly depends on the time constant ฯ.

Discharging Phase (Initial condition: Capacitor pre-charged):

If the capacitor was pre-charged to some voltage (V0) and then the voltage source is suddenly disconnected, the capacitor will start discharging.

In this discharging phase, the capacitor will discharge through the resistor, and the voltage across the capacitor will gradually decrease over time.

The time constant (ฯ) in this case is also determined by the resistance (R) and capacitance (C).

The time it takes for the capacitor to discharge significantly depends on the time constant ฯ.

In both scenarios, the voltage across the capacitor will change over time according to exponential decay. The exact behavior and the rate at which the voltage changes will be determined by the values of resistance (R) and capacitance (C) in the circuit.

It's important to note that if the voltage interruption is sudden and extreme, it may lead to a rapid change in the current flowing through the circuit, which can have consequences depending on the components and their ratings in the circuit. For example, if the current exceeds the component's maximum ratings, it could lead to damage or failure. In practical applications, it's important to consider these factors and implement appropriate protective measures to avoid damaging the circuit.