Equation for Voltage on a capacitor charging through a resistor

The voltage \( V(t) \) across a capacitor \( C \) charging through a resistor \( R \) in a simple RC (resistor-capacitor) circuit can be described by the following equation:

\[ V(t) = V_0 \left(1 - e^{-\frac{t}{RC}}\right) \]

where:
- \( V_0 \) is the supply voltage,
- \( t \) is the time,
- \( R \) is the resistance,
- \( C \) is the capacitance,
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

This equation shows that the voltage across the capacitor increases exponentially over time, approaching the supply voltage \( V_0 \) as \( t \) becomes large.

Would you like more details on this topic or have any other questions?

Here are some questions you might find interesting:
1. How does the time constant \( \tau = RC \) affect the charging process?
2. What is the voltage across the capacitor at \( t = \tau \)?
3. How does the charging curve look graphically?
4. Can you explain the energy stored in the capacitor during charging?
5. What happens in the circuit when the capacitor is fully charged?

**Tip:** Understanding the time constant \( \tau = RC \) is crucial, as it determines how quickly the capacitor charges or discharges.

Understand the equation for voltage on a capacitor charging through a resistor in an RC circuit. Learn about the exponential increase of voltage over time, with detailed explanations of key concepts including resistance, capacitance, and the time constant RC. Suitable for college-level students and enthusiasts of electrical engineering.

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