https://file.aiquickdraw.com/mathbot/file/1730925517413k6aw1leq.jpg

The problem involves a circuit with a capacitor and two resistors, each with a resistance of 200 kΩ, and an initial zero charge on the capacitor. The capacitor has a capacitance of 2 μF, and the battery voltage is 6 V. We need to determine the charge on the capacitor and the current through each component as functions of time.

To solve this, let's proceed with the following steps:

1. **Charge on the Capacitor**: The charge \( Q(t) \) on the capacitor as it charges over time in an RC circuit is given by:
   \[
   Q(t) = C \cdot V \left(1 - e^{-\frac{t}{RC}}\right)
   \]
   where \( C \) is the capacitance, \( V \) is the voltage, and \( R \) is the total resistance in series.

2. **Current in the Circuit**: The current \( I(t) \) as a function of time is:
   \[
   I(t) = \frac{V}{R} \cdot e^{-\frac{t}{RC}}
   \]

### Given values:
- \( C = 2 \, \mu\text{F} = 2 \times 10^{-6} \, \text{F} \)
- \( R = 200 \, \text{k}\Omega + 200 \, \text{k}\Omega = 400 \, \text{k}\Omega = 400 \times 10^3 \, \Omega \)
- \( V = 6 \, \text{V} \)

Would you like me to substitute these values to provide explicit expressions for \( Q(t) \) and \( I(t) \)? 

---

### Related Questions:

1. How does the time constant \( \tau = RC \) affect the charging process?
2. What would happen to \( Q(t) \) and \( I(t) \) if we changed the capacitance?
3. How does the circuit behave if the resistances are not equal?
4. Can we determine the energy stored in the capacitor over time?
5. How does the initial charge on the capacitor impact these calculations?

### Tip:
In RC circuits, the time constant \( \tau = RC \) determines the rate at which the capacitor charges and discharges, representing the time it takes for the capacitor to charge to about 63% of its final value.

El capacitor tiene carga inicial cero, y cada resistencia es de 200 kΩ. Encuentre la carga del capacitor en función del tiempo. También hallar la corriente de cada componente del circuito en función del tiempo.

Analyze the RC circuit with a 2 µF capacitor and two 200 kΩ resistors in series, connected to a 6V battery. Learn to calculate the charge on the capacitor Q(t) and the current I(t) as functions of time, using exponential functions in an RC circuit.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation