# Solve RC Circuit Switch w/ Vs=10V, R1=20kΩ, R2=100kΩ, C1=6μF, C2=12μF

• Engineering
• gfd43tg
In summary, when the switch in the circuit is closed, the voltage across C1 and C2 is 10 V and no current runs through R1 or R2. When the switch is opened at t = 0, the current through R2 becomes zero and remains so for all t ≥ 0. Therefore, i(t) = 0 for all t ≥ 0.
gfd43tg
Gold Member

## Homework Statement

2. The switch in the circuit below had been closed for a long time before it was opened at t = 0. Given that Vs = 10 V, R1 = 20 kΩ, R2 = 100 kΩ, C1 = 6 μF, and C2 = 12 μF, determine i(t) for t ≥ 0.

## The Attempt at a Solution

For this problem, my initial thought is that the voltage must be the same across C1 and C2, since they are open, no current runs through R1 nor R2, so the voltage across both is 10 V. Then, I use the equation for the voltage as a function of time, and get the expression. I then take the derivative and multiply by the equivalent capacitance to get my expression.

I got a negative answer, I'm not sure if this is right. It would mean the current is the opposite direction that I labeled. Would the current go from the larger capacitor to the smaller one?

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If the potentials on the capacitors are identical when the switch opens, what does that tell you about the current through R2?

Yes, the current is zero. Does that mean the current is zero at all times when the switch is turned off? I think my voltage expression is correct, so I just take the derivative to find the current expression.

Maylis said:
Yes, the current is zero. Does that mean the current is zero at all times when the switch is turned off? I think my voltage expression is correct, so I just take the derivative to find the current expression.

Yes, the current is zero. No potential difference across R2 means that no current will flow. If no current flows then the potentials on the capacitors cannot change over time... what does that tell you about i(t) ?

i(t) = 0 for all t?

Maylis said:
i(t) = 0 for all t?

Yup. Well, for all t ≥ 0 that is.

## What is an RC circuit?

An RC circuit is a type of electronic circuit that contains a resistor (R) and a capacitor (C). The resistor controls the flow of current through the circuit, while the capacitor stores electrical charge.

## What is a switch in an RC circuit?

A switch in an RC circuit allows for the control of the flow of current through the circuit. It can be manually operated or controlled by a separate electronic component.

## How do you solve an RC circuit with given values for voltage, resistors, and capacitors?

To solve an RC circuit, you need to use the equations V=IR and Q=CV, where V is the voltage, I is the current, R is the resistance, Q is the charge, and C is the capacitance. You can use these equations to calculate the current and charge at different points in the circuit.

## What is the time constant of an RC circuit?

The time constant of an RC circuit is a measure of how quickly the capacitor charges and discharges. It is calculated by multiplying the resistance (R) and capacitance (C) values together, giving a unit of time (seconds).

## How do you calculate the voltage across a capacitor in an RC circuit?

The voltage across a capacitor in an RC circuit can be calculated using the equation V(t)=Vs(1-e^(-t/RC)), where V(t) is the voltage at a given time (t), Vs is the supply voltage, R is the resistance, and C is the capacitance. This equation takes into account the charge on the capacitor at different times and can be used to plot the voltage over time on a graph.

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