# Current of RC Circuit After Switch is Opened

• Math-U-Up
In summary, the switch has been closed for a long time, so no current flows through the 10 ohm resistor. After a nudge from a helper, the switch does not open and current flows through the battery instead.
Math-U-Up

## Homework Statement

See attached image for circuit diagram and givens.
The switch has been closed for a very long time.
a) What is the charge on the capacitor?
b) The switch is opened at t=0 s. What current initially flows?

V = IR
Q=CV
I=I0e-t/(RC)

## The Attempt at a Solution

Since the switch has been open for a long time, no current flows through the 10 Ohm resistor. Therefore,
I = 100V/(60 Ohm + 40 Ohm) = 1 Amp, V = 1Amp*40 Ohm, and Q = 2uF * 40V = 80uC.

So my question is: Is the current that initially flows after the switch opens at t=0 s just due to the battery? So it would just be 1Amp? I'm having trouble understanding how to find the current at part b.

#### Attachments

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Hello MUU,

First step is to establish where the current flows. Through an open switch ? Or elsewhere ?

Hello @Math-U-Up. Welcome to PF!

Math-U-Up said:

## Homework Statement

See attached image for circuit diagram and givens.
The switch has been closed for a very long time.
a) What is the charge on the capacitor?
b) The switch is opened at t=0 s. What current initially flows?

V = IR
Q=CV
I=I0e-t/(RC)

## The Attempt at a Solution

Since the switch has been open for a long time, no current flows through the 10 Ohm resistor. Therefore,
I = 100V/(60 Ohm + 40 Ohm) = 1 Amp, V = 1Amp*40 Ohm, and Q = 2uF * 40V = 80uC.

So my question is: Is the current that initially flows after the switch opens at t=0 s just due to the battery? So it would just be 1Amp? I'm having trouble understanding how to find the current at part b.
I think you might have misread the problem statement. According to the wording in the problem statement, initially, the switch has been closed for a very long time. That means that current has been flowing through the battery for a very long time.

At time $t = 0$, the switch is opened, meaning that after $t = 0$ no current flows through the battery, and any current flowing in the circuit is the result of whatever residual charge is left in the capacitor.

At least that's the way that I interpret the problem.

(A "closed" switch means that the switch can conduct current. An "open" switch does not conduct current.)

The idea in PF is that the thread poster discovers that after a small nudge from a helper ...

## What is a RC circuit?

A RC circuit is an electrical circuit that contains a resistor (R) and a capacitor (C) connected in series or parallel. It is commonly used in electronic devices for filtering, timing, and signal processing.

## What happens to the current in a RC circuit after the switch is opened?

After the switch is opened, the capacitor will discharge through the resistor, causing the current to decrease over time until it reaches zero. This is because the capacitor acts as a temporary energy storage and releases its charge when the circuit is opened.

## How does the time constant affect the current in a RC circuit?

The time constant, represented by the symbol τ, is the product of the resistance and capacitance in a RC circuit. It determines the rate at which the current decreases after the switch is opened. A larger time constant means a slower decrease in current, while a smaller time constant results in a faster decrease.

## Can the current in a RC circuit after the switch is opened be predicted?

Yes, the current in a RC circuit can be predicted by using the formula I(t) = I₀e^(-t/τ), where I(t) is the current at time t, I₀ is the initial current, and τ is the time constant. This formula follows an exponential decay curve.

## What are some practical applications of RC circuits?

RC circuits have a wide range of applications, such as in audio and video systems, power supplies, and electronic filters. They are also used in timing circuits for electronic devices such as cameras and flash units. In addition, RC circuits are commonly found in electronic toys, remote controls, and electronic ignition systems for vehicles.

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