Question

How to solve the following ??

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.

Answer 1

`0.046` seconds

Explanation:

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`