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

[kcombs]

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!

 

[gneill]

What's the initial current?

 

[kcombs]

What's the initial current?

No value is given.

 

[gneill]

No value is given.

So you will have to calculate it from what is given...

 

[kcombs]

So you will have to calculate it from what is given...

Okay. I can calculate that, but how does voltage come into the picture?

 

[gneill]

Okay. I can calculate that, but how does voltage come into the picture?

What is the initial voltage across the load resistance?

 

[kcombs]

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

 

[gneill]

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?

 

[kcombs]

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!

 

[gneill]

Well done. Glad I could help!