If a capacitor discharges through a resistor, what is the formula for the voltag

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Question: If a capacitor discharges through a resistor, what is the formula for the voltage across the capacitor at time t?

Options:

Correct Answer: V(t) = V0 * e^(-t/RC)

Solution:

The voltage across a discharging capacitor is given by V(t) = V0 * e^(-t/RC).

If a capacitor discharges through a resistor, what is the formula for the voltage across the capacitor at time t?

If a capacitor discharges through a resistor, what is the formula for the voltage across the capacitor at time t?

Step 1: Understand that a capacitor stores electrical energy.
Step 2: Know that when a capacitor discharges, it releases this energy through a resistor.
Step 3: Identify the initial voltage across the capacitor as V0 (the voltage when it starts discharging).
Step 4: Recognize that the time it takes for the capacitor to discharge is represented by 't'.
Step 5: Understand that 'R' is the resistance of the resistor and 'C' is the capacitance of the capacitor.
Step 6: Learn that the formula for the voltage across the capacitor as it discharges is V(t) = V0 * e^(-t/RC).
Step 7: In this formula, 'e' is a mathematical constant approximately equal to 2.71828.

Capacitor Discharge – The process by which a capacitor releases its stored electrical energy through a resistor, resulting in a decrease in voltage over time.
Exponential Decay – The mathematical behavior of the voltage across the capacitor, which decreases exponentially as time progresses.
Time Constant (RC) – The product of resistance (R) and capacitance (C), which determines the rate of voltage decay in the circuit.