Solve RC Circuit Problem: Find Time of Current > 50mA

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Homework Help Overview

The problem involves an RC circuit where a capacitor retains a voltage and a student inadvertently touches its terminals, raising concerns about the current exceeding a dangerous level. The subject area is electrical circuits, specifically focusing on capacitor discharge and current calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the initial current and how to incorporate voltage into the calculations. There are attempts to derive the initial current from the given voltage and resistance, and questions about the relevance of voltage in the context of the problem.

Discussion Status

Some participants have provided guidance on calculating the initial current and have confirmed the correctness of the equations used. There is an ongoing exploration of how to determine the time when the current exceeds 50 mA, with various interpretations of the problem being discussed.

Contextual Notes

Participants note the absence of certain values and express uncertainty about the initial conditions and assumptions regarding the voltage and resistance in the circuit.

kcombs
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Homework Statement


Suppose a 120 micro-farad capacitor from a camera flash unit retains voltage of 210 V when an unwary student removes it from the camera. If the student accidentally touches the two terminals with his hands, and if the resistance of his body between his hands is 1.8 kilo-ohms, for how long will the current across his chest exceed the danger level of 50 mA?

Homework Equations


q(t)=Qe^(-t/(RC))
i(t)=(-Q/(RC))e^(-t/(RC))
V=q/C
i=(dq)/(dt)

The Attempt at a Solution


I'm not sure where the voltage comes into this question. I assume I don't just ignore that piece of given information. I wrote out all the equation, just like above, and I'm not sure how to put them together to find the correct time.

Thanks in advance!
 
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What's the initial current?
 
gneill said:
What's the initial current?

No value is given.
 
kcombs said:
No value is given.
So you will have to calculate it from what is given...
 
gneill said:
So you will have to calculate it from what is given...
Okay. I can calculate that, but how does voltage come into the picture?
 
kcombs said:
Okay. I can calculate that, but how does voltage come into the picture?
What is the initial voltage across the load resistance?
 
gneill said:
What is the initial voltage across the load resistance?
Actually, I'm not sure it's correct but this is what I did:
q=VC
i(t)=(V/R)e^(-t/(RC)) which, due to t=0, simplifies to i(t)=V/R
When I plugged in numbers I got .117 A
 
kcombs said:
Actually, I'm not sure it's correct but this is what I did:
q=VC
i(t)=(V/R)e^(-t/(RC)) which, due to t=0, simplifies to i(t)=V/R
When I plugged in numbers I got .117 A
Yes, the initial current is indeed given by V/R , and your equation for i(t), namely,

i(t)=(V/R)e^(-t/(RC))

looks good.

So now you have an equation for i(t); can you solve for the time when i(t) = 50 mA?
 
gneill said:
Yes, the initial current is indeed given by V/R , and your equation for i(t), namely,

i(t)=(V/R)e^(-t/(RC))

looks good.

So now you have an equation for i(t); can you solve for the time when i(t) = 50 mA?

I just got t=.184 s, which is the correct answer. Thanks for you help! I was definitely overthinking that!
 
  • #10
Well done. Glad I could help!
 

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