How Do RC Circuits Behave with Capacitors and Resistors?

[shemer77]

Homework Statement

http://img301.imageshack.us/img301/9426/55126286.jpg
The cirucit shown has been connecteed for a long time. the battery ahs an internal resistance of 1 ohm.

1) Determine the terminal voltage of teh battery

2) Determine the current in the 4 ohm resistor

3) What is the charge stored on one of the capacitor plates?

4)How long will it take for the 10 ohm resistor to consume as much energy from teh circuit as is stored in the capacitor?

I don't know how to approach this because I don't know what happens when a capacitor is involved.

 

[Delphi51]

After the circuit has been connected for "a long time" you can ignore the capacitor.
It will charge up to whatever voltage is across the 6 ohm resistor and then it will draw zero current thereafter.

 

[nlightner]

I would first start by understanding the components and principles of an RC circuit. An RC circuit is a circuit that contains a resistor and a capacitor connected in series. The resistor (R) limits the flow of current in the circuit, while the capacitor (C) stores electric charge. When a voltage source, such as a battery, is connected to an RC circuit, the capacitor charges up to the same voltage as the battery. This charging process is governed by the time constant, which is equal to the product of the resistance and capacitance (RC).

Now, let's address the questions in the homework statement:

1) To determine the terminal voltage of the battery, we can use Ohm's Law, which states that V = IR, where V is voltage, I is current, and R is resistance. In this case, the internal resistance of the battery is given as 1 ohm, so we can calculate the terminal voltage as V = I(4+1) = 5I. Since the circuit has been connected for a long time, the capacitor is fully charged, and therefore there is no current flowing through the circuit (I = 0). Therefore, the terminal voltage of the battery is 0 volts.

2) The current in the 4 ohm resistor can be calculated using Ohm's Law as well. Since the terminal voltage of the battery is 0 volts, the current in the circuit is also 0 amps. Therefore, the current in the 4 ohm resistor is also 0 amps.

3) To determine the charge stored on one of the capacitor plates, we can use the equation Q = CV, where Q is charge, C is capacitance, and V is voltage. The capacitance of the capacitor is given as 10 microfarads (μF) and we know that the voltage across the capacitor is equal to the terminal voltage of the battery, which is 0 volts. Therefore, the charge stored on one of the capacitor plates is 0 coulombs.

4) The time it takes for the 10 ohm resistor to consume as much energy from the circuit as is stored in the capacitor can be calculated using the time constant (RC). In this case, the time constant is equal to 10 μF x 10 ohms = 100 microseconds (μs). This means that after 100 μs, the energy stored in the capacitor will be completely dissipated by the