Question 5.57: A 150 μF capacitor is charged to a potential of 150 V. The c...

We will solve this problem using the tabular method rather than using the exponential formula.

First we need to find the time constant:

C × R = 150 μF × 2 MΩ = 300 s

Next we find the ratio of t to CR. After 1 minute, t = 60 s, therefore the ratio of t to CR is:

\frac{t}{C R}=\frac{60}{300}=0.2

Referring to the table above,we find that when t/CR = 0.2, the ratio of instantaneous value to final value (k) for decay is 0.8187. Thus:

\frac{v_C }{V_{ S }}=0.8187

or

{v_C} = 0.8187 × 150 = 122.8 V