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 1000 ohm resistor in series with the deflection plates. How long does it take for the potential difference between the deflection plates to reach 50 volts?

Answer:Resistor-Capacitor (RC) circuits, when driven by a voltage/current source, display a type of time-dependent charging or discharging since the charge from the capacitor goes through the resistor. When considering a discharging phase, the time-dependent voltage takes the form

Explanation:

Vt = Voe^-t/RC

Vt equal time dependent voltage

R is the resistance

C is the capacitance of the oscilloscope

Given

Area of capacitor equal to 0.1 * 0.002m

Distance between plates equal 1/1000 = 0.0001m

Vo = 100v supply voltage

Resistance R = : 1000ohms

Vt time dependent voltage = 50V

To find capacitance C = Eo (A/d)

C = (8.85 * 10^-12) * (0.002/0.001)

C = 1.77 * 10^-11

Solving the equation Vt = Voe^-t/RC

t = 0.6931RC

t = 0.6931 (1000) (1.77*10^-11)

t = 1.2*10^-9

t = 1.2ns

It will take the oscilloscope 1.2ns to reach 50V