# Solve RC Circuit Question: Time Constant & Current

• MightyDogg
In summary, the time constant is increased from 150kΩ to only using the 100kΩ resistor after the switch is closed. This causes the current to increase from I=I(e^-t/rc) to I=I(e^-t/0.5rc).
MightyDogg

## Homework Statement

Switch S has been open for a long time. It is then suddenly closed. Determine the time constant (a) before the switch is closed and (b) after the switch is closed. (c) Let the switch be closed at t=0. Determine the current in the switch as a function of time.

T=RC
I=I(e^-t/rc)

## The Attempt at a Solution

I actually already know the answers to this question because of my handy dandy answer key. I know part A is the simple T=RC where R = 50kΩ + 100kΩ and C = 10microF. However, I am confused on part B. Why does the resistance for the time constant change from 150kΩ to only using the 100kΩ resistor?

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MightyDogg said:
Why does the resistance for the time constant change from 150kΩ to only using the 100kΩ resistor?

Do you understand the concept of a short circuit?

No. My professor has not spent much time on the topic. I actually did not know that this problem was a short circuit question.

MightyDogg said:
No. My professor has not spent much time on the topic. I actually did not know that this problem was a short circuit question.

So now that you know, can you make use of the fact ?

Since I do not have any notes on this subject I researched a bit online. From my understanding of what I read, short circuits are circuits that disregard a certain path because the current would rather go along the more unimpeded pathway? However, in this case, why wouldn't the current rather go along the 50kohm resistor since there is less resistance there?

Uh ... how do you get that 50kohm is less than zero?

Wait... I think I have an error in my knowledge of what is fundamentally going on... I was comparing the resistance between 50 and 100. From your reply I am assuming that once the switch closes there can be a current flowing through that loop, so you only need the R for the loop with the least resistance? So that would be the right smaller loop and not the whole one? Sorry for my misunderstandings. I have a test coming up soon and I think I have a decent grasp of the material, it's just my professor never talked about this in class.

Edit: it's just I thought you needed to trace a path from the battery to the capacitor. I guess you do not.

Sounds like you have it now. The closed switch creates a short circuit that takes the voltage source and the 50kohm resistor out of the rest of the circuit. It isn't that the closed switch creates a path with smaller resistance, it creates a path with NO resistance --- that's what a short circuit IS.

Now, the stuff to the left of the short circuit can ALSO be analyzed as a separate circuit, in this case being just a voltage source and a resistor (and not seeing the capacitor and the other resistor at all)

phinds said:
Sounds like you have it now. The closed switch creates a short circuit that takes the voltage source and the 50kohm resistor out of the rest of the circuit. It isn't that the closed switch creates a path with smaller resistance, it creates a path with NO resistance --- that's what a short circuit IS.

Now, the stuff to the left of the short circuit can ALSO be analyzed as a separate circuit, in this case being just a voltage source and a resistor (and not seeing the capacitor and the other resistor at all)

Okay, I understand it now. Thank you for your help!

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

The time constant of an RC circuit is a measure of how quickly the capacitor in the circuit charges or discharges. It is calculated by multiplying the resistance (R) by the capacitance (C) of the circuit.

## How do you calculate the current in an RC circuit?

The current in an RC circuit can be calculated using Ohm's law, which states that current (I) is equal to the voltage (V) divided by the resistance (R). In an RC circuit, the resistance is constantly changing as the capacitor charges or discharges, so the current will also change over time.

## What happens to the current over time in an RC circuit?

In an RC circuit, the current decreases over time as the capacitor charges. This is because as the capacitor charges, it becomes more difficult for current to flow through it. Eventually, the current will reach zero once the capacitor is fully charged.

## How does the size of the capacitor affect the time constant in an RC circuit?

The time constant of an RC circuit is directly proportional to the size of the capacitor. This means that a larger capacitor will have a longer time constant, resulting in a slower charging or discharging process.

## What is the practical application of RC circuits?

RC circuits have many practical applications, such as in filters, oscillators, and timing circuits. They are also used in electronic devices to smooth out signals and prevent damage from sudden changes in current.

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