Find Time Constant for RC Circuit: Solve the Equation!

In summary, the time constant of charging for the capacitor shown in the figure is 0, as all components are in parallel and have the same potential difference. This is due to the ideal voltage source and negligible resistance in the wires. Therefore, the capacitor voltage immediately after the switch closes is V, resulting in a time constant of 0.
  • #1
utkarshakash
Gold Member
854
13

Homework Statement


The time constant of charging for the capacitor shown in the figure is


Homework Equations



See attached diagram

The Attempt at a Solution



[itex]\tau = R_{eq} C [/itex]

[itex]R_{eq} = R/2 [/itex]

So the answer should be t= RC/2. But the correct answer is 0! :confused:
 

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  • #2
Once the switch is closed all the components are in parallel, right? What's the rule for the potential across components in parallel?
 
  • #3
gneill said:
Once the switch is closed all the components are in parallel, right? What's the rule for the potential across components in parallel?

They all have the same potential difference.
 
  • #4
utkarshakash said:
They all have the same potential difference.

Right. And if the voltage source is ideal and the wires have entirely negligible resistance, then the capacitor voltage immediately after the switch closes must be...
 
  • #5
gneill said:
Right. And if the voltage source is ideal and the wires have entirely negligible resistance, then the capacitor voltage immediately after the switch closes must be...

It should be V. Thus time constant must be 0. Thanks !
 

FAQ: Find Time Constant for RC Circuit: Solve the Equation!

What is the time constant for an RC circuit?

The time constant for an RC circuit is equal to the product of the resistance (R) and the capacitance (C), denoted as RC.

How do you solve the equation for finding the time constant of an RC circuit?

The equation for finding the time constant of an RC circuit is τ = RC. To solve for the time constant, you need to know the values of R and C and plug them into the equation.

Why is it important to find the time constant in an RC circuit?

The time constant is an important parameter in an RC circuit as it determines the rate at which the capacitor charges or discharges. It also helps in predicting the behavior of the circuit over time.

What are the units of the time constant?

The time constant has units of seconds (s) when the values of resistance and capacitance are in standard units (ohms and farads, respectively).

Can the time constant of an RC circuit be changed?

Yes, the time constant can be changed by altering the values of either the resistance or the capacitance. Increasing the resistance or decreasing the capacitance will result in a longer time constant, while decreasing the resistance or increasing the capacitance will result in a shorter time constant.

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