Find the initial current in the circuit (at t=0)

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Homework Help Overview

The discussion revolves around a circuit problem involving a capacitor discharging through a resistor. The initial charge on the capacitor is given, and participants are tasked with determining the initial current at the moment the switch is closed.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of closing the switch at t=0, with some asserting that no current flows initially, while others question this assumption and seek clarification on the voltage and capacitance involved.

Discussion Status

Multiple interpretations of the initial current are being explored. Some participants have provided calculations and reasoning regarding the relationship between charge, voltage, and current, while others have pointed out potential misunderstandings regarding the definitions of charge and current.

Contextual Notes

There are ongoing questions about the capacitance of the capacitor and the assumptions made about the current flow at the moment the switch is closed. The calculations presented involve the time constant and Kirchhoff's voltage law, but there is no consensus on the initial current value.

Fatima Hasan
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Homework Statement


In the circuit shown,the initial charge on the capacitor is Q0 = 200μC . If the switch is closed at t=0 , the capacitor starts discharging through the resistance R=4MΩ . What is the initial current (in μA) (i.e. at t=0) in the circuit?
53_ABA506-64_E0-4721-_B028-006_CDE9_A64_A4.jpg

Homework Equations


I = I0 e-t/τ
τ = Req *C
Q = CΔV

The Attempt at a Solution


When the switch is closed at t=0 , no current will flow .
I = 0
Is my answer correct ?
 

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Fatima Hasan said:
The initial current
Initial charge.
Fatima Hasan said:
When the switch is closed at t=0 , no current will flow .
Why not? What is the voltage?
 
Fatima Hasan said:

Homework Statement


The initial current on the capacitor is Q0 = 200μC . If the switch is closed at t=0 , the capacitor starts discharging through the resistance R=4MΩ . What is the initial current (in μA) (i.e. at t=0) in the circuit?

What is the capacitance of that capacitor? And the 200 μC is charge, not current.
Fatima Hasan said:

The Attempt at a Solution


When the switch is closed at t=0 , no current will flow .
I = 0
Is my answer correct ?
No. The current is zero when the switch is open, but starts to flow just at the instant it is closed. How does the current change with time in case of a discharging capacitor?
 
haruspex said:
Initial charge.

Why not? What is the voltage?
ehild said:
What is the capacitance of that capacitor? And the 200 μC is charge, not current.

No. The current is zero when the switch is open, but starts to flow just at the instant it is closed. How does the current change with time in case of a discharging capacitor?

τ =Req C
= 4*106 * 2*10-6
τ= 8s
Using KVL :
-RI + Vc = 0
Vc = Q / C
- 4*106 * I + (200 μ)/(2μ) =0
I = 2.5*10-5 = 25 μA
I = I0 e-t/τ
2.5*10-5 = I0 e0/8
I0 = 2.5*10-5
= 25 μA
 
Fatima Hasan said:
τ =Req C
= 4*106 * 2*10-6
τ= 8s
Using KVL :
-RI + Vc = 0
Vc = Q / C
- 4*106 * I + (200 μ)/(2μ) =0
I = 2.5*10-5 = 25 μA
I = I0 e-t/τ
2.5*10-5 = I0 e0/8
I0 = 2.5*10-5
= 25 μA
Right answer, but it is much simpler than that.
You know the charge and capacitance, so what is the potential? What current results when that potential is placed across that resistance?
 
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Fatima Hasan said:
τ =Req C
= 4*106 * 2*10-6
τ= 8s
Using KVL :
-RI + Vc = 0
Vc = Q / C
- 4*106 * I + (200 μ)/(2μ) =0
I = 2.5*10-5 = 25 μA
I = I0 e-t/τ
2.5*10-5 = I0 e0/8
I0 = 2.5*10-5
= 25 μA
it is correct now. :smile:
 
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