The deflection plates in an oscilloscope are 10 cm by 2 cm with a gap distance of 1 mm. A 100 volt potential difference is suddenly applied to the initially uncharged plates through a 975 ohm resistor in series with the deflection plates. How long does it take for the potential difference between the deflection plates to reach 75 volts

Answer: 23.92 ns

Explanation:

The capacitance, C = (e (0) * A) / d

C = [8.85*10^-12 * 2*10^-2 * 10*10^-2] / 1*10^-3

C = (1.77*10^-14) / 1*10^-3

C = 1.77*10^-11

C = 17.7 pF

Vc = V * [1 - e^ - (t/CR) ]

75 = 100 * [1 - e^ - (t/CR) ]

75/100 = 1 - e^ - (t/CR)

e^ - (t/CR) = 1 - 0.75

e^ - (t/CR) = 0.25

If we take the log of both sides, we then have

Log e^ - (t/CR) = Log 0.25

-t/CR = In 0.25

t = - CR In 0.25

t = - 17.7*10^-12 * 975 * - (1.386)

t = 2.392*10^-8 s

t = 23.92 ns