How to solve the following ??

Question

In a condenser discharging electricity, the voltage 'V' satisfies the equation : #k((dV)/dt) + V = 0# where, 'k' is a constant 'C', 't' is the time measured in seconds. Given #k = 50#. Find the time 't' in which 'V' decreases to #(1/10)^(th)# of it's original value.

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Answer 1 · 2018-04-26T13:19:27

#0.046# seconds

The equation can be rewritten in the form

#(dV)/V = -kdt#

which can be easily integrated to

#int_(V_0)^V (dV)/V = -int_0^t kdt#

#ln(V/V_0) = -kt implies t = 1/kln(V_0/V)#

Substituting #k=50# and #V_0/V = 10#, we get

#t = 1/50 ln10=0.046#