Time constant for parallel RC circuit

In summary, the question asks for the value of the time constant in a circuit with a capacitor and a net resistance of 1/2R. The correct answer is RC, but the student thought it should be 1/2 RC. The mentor explains that the total resistance in series with the capacitor is what shows up in the time constant and suggests using differential equations to understand this concept. The mentor also poses a bonus question about the effect of an ideal voltage source on the time constant.
  • #1
Shivang kohlii
19
1

Homework Statement



Question 6.
IMG-20190103-WA0005.jpeg


Homework Equations


Time constant = RC

The Attempt at a Solution


I think answer should be 1/2 RC as Rnet = 1/2R and to convert it to single resistance form we should first find Rnet
But the answer is coming out to be RC . How?

<< Corrected Image added by Mentors >>

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  • #2
Shivang kohlii said:
But the answer is coming out to be RC . How?
What is the total resistance in series with the Capacitor? That is the resistance that shows up in the time constant (assuming the voltage source is ideal)...

Are you familiar with Differential Equations? That would be one way to show how this works in this circuit...
 
  • #3
Bonus Question -- What if the voltage source is not ideal? How would that change things? :smile:
 

1. What is the formula for calculating the time constant of a parallel RC circuit?

The time constant (τ) of a parallel RC circuit is calculated using the formula τ = RC, where R is the resistance in ohms and C is the capacitance in farads.

2. How does the time constant affect the behavior of a parallel RC circuit?

The time constant determines the rate at which the capacitor charges and discharges in a parallel RC circuit. A larger time constant means a slower charging and discharging process, while a smaller time constant results in a faster process.

3. Can the time constant be changed in a parallel RC circuit?

Yes, the time constant can be changed by altering either the resistance or capacitance in the circuit. Increasing the resistance or capacitance will result in a larger time constant, while decreasing them will result in a smaller time constant.

4. What is the significance of the time constant in a parallel RC circuit?

The time constant is an important parameter in understanding the behavior of a parallel RC circuit. It helps determine the charging and discharging times, as well as the stability of the circuit.

5. How does the time constant change when capacitors are added in parallel in a circuit?

When capacitors are added in parallel in a circuit, the overall capacitance increases and therefore the time constant decreases. This means that the circuit will charge and discharge faster compared to when there was only one capacitor in the circuit.

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