Large capacitors can hold a potentially dangerous charge long after a circuit ha

Question

Large capacitors can hold a potentially dangerous charge long after a circuit has been turned off, so it is important to make sure they are discharged before you touch them. Suppose a 120 Fcapacitor from a camera flash unit retains a voltage of 180 V when an unwary student removes it from the camera.

1. If the student accidentally touches the two terminals with his hands, and if the resistance of his body between his hands is 1.8 k, for how long will the current across his chest exceed the danger level of 50 mA?

Explanation / Answer

C = 120 uF = 120 x 10^-6 F ; V = 180 V ; R = 1.8 k Ohm = 1.8 x 10^3 Ohm ; I = 50 mA ; I = 50 mA = 0.05 A

This forms a capacitive circuit.

The maximum curent in this circuit can be:

I = V/R = 180/1800 = 0.1 A

time constant is : T = RC = 1800 x 120 x 10^-6 = 0.216

We know that, for a capacitive circuit at any time t

I = I(max) e^-t/RC

0.05 = 0.1 x e^-t/0.216

e^-t/0.216 = 0.5

taking natural long both sides

-t/0.216 = -0.693

t = 0.693 x 0.216 = 0.149 s

Hence, time required = 0.149 s = 149 milli-sec

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