# Suppose that electricity is draining from a capacitor at a rate that is proportional to the volt-age V across its terminals and that, if t is measured in seconds,dV /dt= -1/ 40Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?

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Suppose that electricity is draining from a capacitor at a rate that is proportional to the volt-age V across its terminals and that, if t is measured in seconds,

dV /dt= -1/ 40

Solve this equation for V, using V0 to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?

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Step 1

Separate the variables.

Step 2

Integrate both sides

Step 3

Given at t=0, V=V0

Using...

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