You have an RC circuit and you measure the "zero" voltage to actually be 2.385 [Volts].
The peak voltage is measured to be 8.262 [Volts].
At what voltage value will you look for t4 = time stamp for 15/16 total charge?
To find the voltage value at t4 for 15/16 total charge in an RC circuit, we need to calculate the time constant of the circuit and use it to determine the time at which the charge reaches the desired fraction.
First, let's define a few key terms:
- Zero voltage (V0): The voltage when the circuit is initially discharged.
- Peak voltage (VP): The maximum voltage reached in the circuit during charging.
The time constant (τ) of an RC circuit is given by the equation:
τ = RC
where R is the resistance and C is the capacitance of the circuit.
Given that the zero voltage (V0) is 2.385 V and the peak voltage (VP) is 8.262 V, we can express the voltage at any time (t) during charging using the equation:
V(t) = V0 + (VP - V0) * (1 - e^(-t/τ))
The fraction of charge at a given time (t) is given by the equation:
q(t) = 1 - e^(-t/τ)
We need to find the time (t4) at which the charge reaches 15/16 (or 0.9375) of the total charge, which means q(t4) = 0.9375.
Let's solve for t4 using the equation for the fraction of charge:
0.9375 = 1 - e^(-t4/τ)
Rearranging the equation, we have:
e^(-t4/τ) = 1 - 0.9375
Taking the natural logarithm (ln) of both sides, we get:
-t4/τ = ln(1 - 0.9375)
Solving for t4, we have:
t4 = -τ * ln(1 - 0.9375)
Now, substitute the value of τ with RC, where R is the resistance and C is the capacitance of the circuit.
Finally, plug in the values of R and C into the equation and evaluate t4 to find the voltage value at that time.
To find the voltage value at t4, which corresponds to 15/16 of the total charge, we need to use the RC charging equation. The equation is given by:
V(t) = V_p * (1 - e^(-t/RC))
Where:
V(t) is the voltage at time t
V_p is the peak voltage
t is the time
R is the resistance of the circuit
C is the capacitance of the circuit
In this case, we are given the zero voltage and the peak voltage. We can use this information to find the time constant (RC) as follows:
V(0) = V_p * (1 - e^(-0/RC))
2.385 = 8.262 * (1 - e^0)
e^0 = 1
2.385/8.262 = 1 - 1
1 - 1 = 0
0 = 0
Since we have an equation that equals 0, this means that the time constant (RC) will not affect the solution. Therefore, we can simply proceed with finding the time at 15/16 of the total charge.
15/16 of the total charge corresponds to a voltage of:
V(t4) = V_p * (1 - 15/16)
V(t4) = 8.262 * (1 - 15/16)
V(t4) = 8.262 * (16/16 - 15/16)
V(t4) = 8.262 * (1/16)
V(t4) = 0.516375
Therefore, the voltage value at t4 for 15/16 of the total charge is approximately 0.516375 [Volts].