yogotah said:Homework Statement
How many time constants must elapse if an initially charged capacitor is to discharge 55% of its stored energy through a resistor?
Homework Equations
The Attempt at a Solution
I don't even know where to start, so please a nudge in the right direction would help.
Thanks!
The time constant, denoted by the symbol τ, is equal to the product of the resistance and capacitance in a circuit. It represents the amount of time it takes for a capacitor to charge to approximately 63.2% of its maximum voltage. Therefore, it takes approximately 5 time constants for a capacitor to fully charge.
If a voltage is applied to a capacitor for less than one time constant, the capacitor will not have enough time to charge to its full capacity. This is because the capacitor's charging rate is directly proportional to the time constant. So, if less time elapses, the capacitor will charge to a lower voltage.
Technically, a capacitor can never be fully charged. This is because it is impossible to have an infinite amount of time to charge a capacitor. However, after 5 time constants, the capacitor will be charged to approximately 99.3% of its maximum voltage, which is considered fully charged for practical purposes.
Yes, the size of a capacitor, specifically its capacitance, directly affects the number of time constants needed to charge it. A larger capacitance will require more time constants to fully charge, while a smaller capacitance will require fewer time constants.
Yes, the number of time constants needed to discharge a capacitor can be calculated using the same formula as the charging time constant. However, it is important to note that the discharge time constant will be different from the charging time constant due to the different factors involved in the discharge process.