If a capacitor discharges through a resistor, what is the voltage across the cap

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Question: If a capacitor discharges through a resistor, what is the voltage across the capacitor after one time constant?

Options:

Correct Answer: V0/e

Solution:

After one time constant (τ), the voltage across the capacitor will be V0/e, where V0 is the initial voltage.

If a capacitor discharges through a resistor, what is the voltage across the capacitor after one time constant?

If a capacitor discharges through a resistor, what is the voltage across the capacitor after one time constant?

Step 1: Understand that a capacitor stores electrical energy and has an initial voltage, V0.
Step 2: Know that when a capacitor discharges, it releases its stored energy through a resistor.
Step 3: Learn about the time constant (τ), which is a measure of how quickly the capacitor discharges.
Step 4: After one time constant (τ), the voltage across the capacitor decreases.
Step 5: The formula for the voltage across the capacitor after one time constant is V0/e.
Step 6: Recognize that 'e' is a mathematical constant approximately equal to 2.718.
Step 7: Therefore, after one time constant, the voltage across the capacitor is V0 divided by e.

Capacitor Discharge – Understanding the behavior of a capacitor discharging through a resistor, specifically the exponential decay of voltage over time.
Time Constant (τ) – The time constant is defined as τ = RC, where R is resistance and C is capacitance, indicating the time it takes for the voltage to drop to approximately 36.8% of its initial value.
Exponential Decay – The concept that the voltage across the capacitor decreases exponentially over time, which is a key characteristic of RC circuits.