When a camera flash goes off, the batteries immediately begin to recharge the fl

Question

When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by the following. Q(t) = Q0(1 - e^-t/a) (The maximum charge capacity is Q0 and t is measured in seconds.) (a) Find the inverse of this function. Explain its meaning. This gives us the charge Q obtained within a given time t. This gives us the time t with respect to the maximum charge capacity Q0. This gives us the time t necessary to obtain a given charge Q. (b) How long does it take to recharge the capacitor to 85% of capacity if a = 8? (Round your answer to one decimal place.)

Explanation / Answer

here,

(a)

Q(t) = Q0 (1-e^-t/a)

solving the equation ,

Q(t)/Q0 = (1-e^-t/a)

t(Q) = - a * ln(1 - (Q(t)/Q0))

this gives us the time t to obtain a given charge Q

(b)

Q = 0.85 * Q0

a = 8

the time taken , t(Q) = a * ln(1 - (Q(t)/Q0))

t(Q) = - 8 * ln(1 - ( 0.85 * Q0/Q0))

t(Q) = 15.18 s

the time taken to recharge the capacitor 85% of capacity is 15.18 s

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