A series electrical circuit for a computer game which you are testing, features a capacitor (C) discharging via a 270 resistor (R). The capacitor is initially charged to a voltage of 15 V. The voltage across the capacitor (Vc) may be described by the following equation, where t represents time.

Vc = 15 􁉀e−𝑡𝑡
􀵗𝑅𝑅𝑅𝑅􁉁
The circuit produces an output based upon the time it takes for the voltage on the capacitor to discharge to a
value of 2 V. The value of the capacitance is based upon the year of your birth, which is input at the start of the
game. For example, if you were born in 1987, then C = 1 + 9 + 8 + 7 = 25 μF.
Determine how long it takes for the circuit to produce an output.
Original post by Tj1996
A series electrical circuit for a computer game which you are testing, features a capacitor (C) discharging via a 270 resistor (R). The capacitor is initially charged to a voltage of 15 V. The voltage across the capacitor (Vc) may be described by the following equation, where t represents time.

Vc = 15 􁉀e−𝑡𝑡
􀵗𝑅𝑅𝑅𝑅􁉁
The circuit produces an output based upon the time it takes for the voltage on the capacitor to discharge to a
value of 2 V. The value of the capacitance is based upon the year of your birth, which is input at the start of the
game. For example, if you were born in 1987, then C = 1 + 9 + 8 + 7 = 25 μF.
Determine how long it takes for the circuit to produce an output.

Welcome to TSR, please describe what have you done and explain the difficulties that you faced.

Is the equation
Vc = 15 􁉀e−𝑡𝑡
􀵗𝑅𝑅𝑅𝑅􁉁
this
$V_{\text{C}} = 15 e^{-\frac{t}{RC}}$ ?
The equation seems to have got a bit mangled.

Probably it should be

Vc=15 e^-t/RC
Which is the usual way for writing the capacitor discharge equation

15 is from the 15V original PD on the capacitor.
RC is known as the time constant of the circuit.
We're told to find the value of t at which Vc = 2V

You could start by dividing by 15 and then taking the natural log (log base e)
Original post by Eimmanuel
Welcome to TSR, please describe what have you done and explain the difficulties that you faced.
Is the equation
Vc = 15 􁉀e−𝑡𝑡
􀵗𝑅𝑅𝑅𝑅􁉁
this
$V_{\text{C}} = 15 e^{-\frac{t}{RC}}$ ?
hi yes sorry for the format, that is the equation but after 15 its in brackets. ive not done this in around 15 years so i am very rusty to say the least, and im finding the whole equation hard to get to grips with and i cant seem to understand why
Original post by Tj1996
hi yes sorry for the format, that is the equation but after 15 its in brackets. ive not done this in around 15 years so i am very rusty to say the least, and im finding the whole equation hard to get to grips with and i cant seem to understand why

It seems that you want to know how to do the maths. If yes, you can watch the following video.

https://youtu.be/fSO8nRx9YaQ?si=HBe58JUaA4EMt9DX

If you want to know more about "physics", you can watch the following video.

https://youtu.be/eCOLkUPSpxc?si=4f2b7hFPt9o4Tqdl