How Do I Calculate the Charge Over Time in Simple RC Circuits?

The resulting equations should yield a differential equation for the capacitor voltage.In summary, the first circuit with Battery B, Resistors R1, R2, and Capacitor C is equivalent to the second circuit with combined R1 and R2, in terms of calculating the capacitor voltage versus time. To get the charge as a function of time for the first circuit, write KCL equations for each node and solve the resulting differential equation. For the third circuit, write KCL equations for each node, including the node between the bottom R and the capacitor, to get a differential equation for the capacitor voltage.
  • #1
stephencohorn
2
0
Ok, if I have a Battery B, Resistors R1, R2, and Capacitor C in this circuit:
(the ...'s just represent empty space, spaces were getting eaten when I previewed the post)

|----------R1--------|
|......|
B+......|
B-......C
|......|
|---------R2---------|

is this equivalent to:

|--------R1--------R2---|
|.......|
B+......C
B-......|
|.......|
|------------------------|

if not, how would you get the charge as a function of time for the first circuit?
also, how would you get the charge as a function of time for the following circuit?

|---------------|---------|
|.....|....|
|.....C...|
B+......|...R
B-......R...|
|.....|...|
|-------------------------|

any conceptual comments on how these two would compare speaking of rate of chargeing, final charge, etc?

Any help would be appreciated, I'm struggling with this stuff.
Thanks,
Stephen
 
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  • #2
please can you help me to solve my problem
 
  • #3
can anyone help me out?
 
  • #4
Combining R1 and R2 in the first circuit to make the 2nd circuit is fine, if you are wanting to calculate the capacitor voltage versus time.

For the 3rd circuit, you will need to write the KCL equations for each of the nodes, including the node between the bottom R and the capacitor.
 

What is a simple RC circuit?

A simple RC (resistor-capacitor) circuit is an electronic circuit that consists of a resistor and a capacitor connected in series or parallel. It is commonly used to filter or delay signals in electronic devices.

How do you calculate the time constant of a simple RC circuit?

The time constant of a simple RC circuit is calculated by multiplying the resistance value of the resistor (in ohms) by the capacitance value of the capacitor (in farads). The resulting value is the time constant in seconds.

What is the purpose of a resistor in a simple RC circuit?

A resistor in a simple RC circuit is used to limit the flow of current and control the voltage in the circuit. It also helps in dissipating heat and protecting the other components from damage.

How does a capacitor affect the behavior of a simple RC circuit?

A capacitor in a simple RC circuit stores and releases electrical energy in the form of a charge. This causes a delay in the flow of current, which results in a time-dependent behavior of the circuit, such as filtering or smoothing of signals.

What are some real-life applications of simple RC circuits?

Simple RC circuits are commonly used in electronic devices such as radios, amplifiers, and filters. They can also be found in timing circuits, power supplies, and electronic flash units. In addition, they are used in various medical devices, such as pacemakers and defibrillators.

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