Math Problem Statement

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

Solution

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

V(t)=V0etRCV(t) = V_0 \cdot e^{-\frac{t}{RC}}

where:

  • V0V_0 is the initial voltage across the capacitor at t=0t = 0,
  • RR is the resistance in ohms,
  • CC is the capacitance in farads,
  • tt is the time in seconds after the circuit starts discharging.

Explanation

  1. Starting Condition: At t=0t = 0, the voltage across the capacitor is V0V_0.
  2. Exponential Decay: As the circuit discharges, the voltage decreases exponentially over time, with a time constant τ=RC\tau = RC.
  3. Time Constant τ\tau: The time constant RCRC represents the time it takes for the voltage to drop to approximately 36.8% of its initial value.

Thus, by substituting tt, RR, and CC into the formula, you can calculate the voltage V(t)V(t) at any moment during the discharging process.

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


  1. How do you determine the time constant τ\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 RR 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 τ=RC\tau = RC is a key factor; it dictates how quickly the circuit discharges.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponential Decay
RC Circuits
Time Constant in RC Circuits

Formulas

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

Theorems

Exponential Decay Formula
Time Constant (τ) for RC Circuits

Suitable Grade Level

Undergraduate