Some lamps are made to turn on or off when the base is touched. These lamps use

Question

Some lamps are made to turn on or off when the base is touched. These lamps use a one-terminal variation of the capacitive switch circuit. Consider the circuit below which shows a circuit model of such a lamp. Suppose it is given that Cois 24 pF. What is the change in v(t) when a person touches the lamp. Express your answer as a fraction of vs(t); in other words it should be a number between 0 and 1. Express your answer to four decimal places.

Some lamps are made to turn on or off when the base is touched. These lamps use a one-terminal variation of the capacitive switch circuit. Consider the circuit below which shows a circuit model of such a lamp. Suppose it is given that Cois 24 pF. What is the change in v(t) when a person touches the lamp. Express your answer as a fraction of vs(t); in other words it should be a number between 0 and 1. Express your answer to four decimal places.

Explanation / Answer

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Before the person touches :

V(t) = Vs(t)(24 pF/(24 pF + 10 pF))

V(t) = 12/17 Vs(t) .

Now if he touches the lamp :

The series capacitance of (100 + 10) pF = 100/11 pF comes in parallel with 10 pF .

Then Ceq = (10 pF) II (100/11 pF) = (10 + 100/11) = 210/11 pF

Thus V(t) = Vs(t) (210/11/(10 + 210/11)) = 210/320 Vs(t)

V(t) = -(0.0496) Vs(t)   

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