If a capacitor is charged to a voltage V and then connected to a resistor R, wha

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Question: If a capacitor is charged to a voltage V and then connected to a resistor R, what is the time constant of the circuit?

Options:

Correct Answer: RC

Solution:

The time constant τ of an RC circuit is given by τ = R * C.

If a capacitor is charged to a voltage V and then connected to a resistor R, what is the time constant of the circuit?

If a capacitor is charged to a voltage V and then connected to a resistor R, what is the time constant of the circuit?

Step 1: Understand that a capacitor stores electrical energy when charged to a voltage V.
Step 2: Know that when the charged capacitor is connected to a resistor R, it will discharge through the resistor.
Step 3: Learn that the time constant (τ) is a measure of how quickly the capacitor discharges.
Step 4: Remember the formula for the time constant in an RC circuit: τ = R * C.
Step 5: Identify that R is the resistance in ohms and C is the capacitance in farads.
Step 6: Calculate the time constant by multiplying the resistance (R) by the capacitance (C).

Time Constant in RC Circuits – The time constant τ represents the time it takes for the voltage across the capacitor to either charge or discharge to approximately 63.2% of its maximum value.
Relationship between Resistance and Capacitance – The time constant is directly proportional to both the resistance (R) and the capacitance (C) in the circuit.