How Long for Potential Difference to Reach 50 Volts in an Oscilloscope?

[sdevoe]

Homework Statement

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 900 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?

Homework Equations

q=c*(delta_V)

The Attempt at a Solution

There has to be an equation that I am missing or need

 

[rl.bhat]

The whole problems converts into a RC circuit.
Find the expression for the charging of the capacitance.

 

[nlightner]

to use.

As a scientist, it is important to understand the concept of potential difference and how it relates to electric fields. In this scenario, we have a set of deflection plates in an oscilloscope that are initially uncharged and have a gap distance of 1 mm. The plates have a length of 10 cm and a width of 2 cm. A 100 volt potential difference is suddenly applied to the plates through a 900 ohm resistor in series.

To calculate the time it takes for the potential difference between the plates to reach 50 volts, we need to use the equation q = C * ΔV, where q is the charge, C is the capacitance, and ΔV is the potential difference. In this case, we know the potential difference (100 volts) and the capacitance (given by the dimensions of the plates), but we do not know the charge.

We can use Ohm's law (V = IR) to determine the current (I) flowing through the circuit. Since the potential difference is 100 volts and the resistance is 900 ohms, the current is equal to 100/900 = 0.1111 amps.

Next, we can use the equation q = It, where q is the charge, I is the current, and t is the time. Since we know the current and the charge (from the previous equation), we can rearrange the equation to solve for t: t = q/I.

Plugging in the known values, we get t = (100 volts * 10 cm * 2 cm * 8.85 x 10^-12 F/m * 1 mm)/0.1111 amps. This gives us a time of approximately 1.99 x 10^-9 seconds for the potential difference between the plates to reach 50 volts.

It's important to note that this calculation assumes ideal conditions and does not take into account any external factors that may affect the time it takes for the potential difference to reach 50 volts. However, it gives us a good estimate based on the given parameters.