How long does it take for a 10 motivated capacitor with a 1 megaohm resistor in series to charge to 67% (1 time constant) of the applied voltage?
I meant microfarad
10 motivated capacitor
you mean microfarad?
check out the RC constant definition.
http://www.electronics-tutorials.ws/rc/rc_1.html
To determine the time it takes for a capacitor to charge to a certain percentage of the applied voltage, we need to use the concept of time constants.
The time constant, denoted as τ (tau), is the time it takes for a capacitor to charge or discharge to approximately 63.2% of the applied voltage.
In this case, you are asking about charging to 67% of the applied voltage, which is very close to one time constant.
To calculate the time constant, we use the formula:
τ = R * C
Where:
τ is the time constant,
R is the resistance in ohms,
C is the capacitance in farads.
Given that the capacitor has a capacitance of 10 microfarads (10 μF) and the resistor has a resistance of 1 megaohm (1 MΩ), we can plug these values into the formula:
τ = (1 MΩ) * (10 μF)
Let's simplify the units to ohms and farads:
τ = 1,000,000 Ω * 0.00001 F
τ = 10 seconds
So, the time constant (τ) for this circuit is 10 seconds.
Since 1 time constant represents approximately 63.2%, to find the time it takes for the capacitor to charge to 67% of the applied voltage, we can multiply the time constant by 1:
Time = 1 * τ
Time = 1 * 10 seconds
Time = 10 seconds
Therefore, it will take approximately 10 seconds for the capacitor to charge to 67% (1 time constant) of the applied voltage in this circuit.