Find Time Constant for RC Circuit: Solve the Equation!

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SUMMARY

The time constant for an RC circuit is defined by the equation τ = R_eq C, where R_eq is the equivalent resistance. In this discussion, R_eq is calculated as R/2, leading to an initial conclusion of t = RC/2. However, it is established that once the switch is closed, all components are in parallel, resulting in an immediate potential across the capacitor, which leads to a time constant of 0 due to the ideal voltage source and negligible wire resistance.

PREREQUISITES
  • Understanding of RC circuit theory
  • Familiarity with the concept of time constant in electrical circuits
  • Knowledge of parallel circuit rules
  • Basic principles of ideal voltage sources
NEXT STEPS
  • Study the implications of ideal voltage sources on circuit behavior
  • Learn about the characteristics of parallel circuits in depth
  • Explore the derivation and applications of the time constant in various RC configurations
  • Investigate the effects of non-ideal components on time constants in circuits
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Electrical engineering students, educators teaching circuit theory, and professionals working with RC circuits and time constant calculations.

utkarshakash
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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



\tau = R_{eq} C

R_{eq} = R/2

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

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Once the switch is closed all the components are in parallel, right? What's the rule for the potential across components in parallel?
 
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.
 
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...
 
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 !
 

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