how to find the voltage of a discharging rc circuit (i know v0, r, and c)

To find the voltage \( V(t) \) across a discharging resistor-capacitor (RC) circuit, you can use the formula:

\[
V(t) = V_0 \cdot e^{-\frac{t}{RC}}
\]

where:
- \( V_0 \) is the initial voltage across the capacitor at \( t = 0 \),
- \( R \) is the resistance in ohms,
- \( C \) is the capacitance in farads,
- \( t \) is the time in seconds after the circuit starts discharging.

### Explanation
1. **Starting Condition**: At \( t = 0 \), the voltage across the capacitor is \( V_0 \).
2. **Exponential Decay**: As the circuit discharges, the voltage decreases exponentially over time, with a time constant \( \tau = RC \).
3. **Time Constant \( \tau \)**: The time constant \( RC \) represents the time it takes for the voltage to drop to approximately 36.8% of its initial value.

Thus, by substituting \( t \), \( R \), and \( C \) into the formula, you can calculate the voltage \( V(t) \) at any moment during the discharging process.

Would you like more details on exponential decay or the time constant in RC circuits?

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1. How do you determine the time constant \( \tau \) in RC circuits?
2. What happens to the voltage as time approaches infinity in a discharging RC circuit?
3. How does changing the resistance \( R \) affect the rate of voltage decay?
4. How can we find the initial current in a discharging RC circuit?
5. How would the formula change if it were a charging RC circuit?

**Tip**: The time constant \( \tau = RC \) is a key factor; it dictates how quickly the circuit discharges.

Learn how to calculate the voltage across a discharging RC circuit over time using exponential decay. Given V0, resistance (R), and capacitance (C), this guide explains the formula V(t) = V0 * e^(-t / RC) and the role of the time constant (τ = RC) in determining voltage decay. Suitable for undergraduate-level students studying physics or electrical engineering.

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