Need help finding voltage across a capacitor in an RC circuit?

In summary, the conversation discusses finding the voltage across a capacitor in an RC circuit using the given initial voltage and function. The equations dV/dt = (1/RC)(V)=(1/RC)([V]_{}[/in]) and VC = V0(1− e−t /τ ) are mentioned as well as the use of differential equations to solve for the desired voltage. The concept of time constant and the equations for voltage across a resistor and capacitor are also mentioned as helpful in solving the problem.
  • #1
sl02ggp
7
0
1. Homework Statement

Find the voltage across a capacitor in an RC Circuit, using [V]_{}[/c] (0) = 1, [V]_{}[/i] n(t)=t.

2. Homework Equations
dV/dt = (1/RC)(V)=(1/RC)([V]_{}[/in])


3. The Attempt at a Solution
New to this site: I honestly don't know where to start. Done well in Calculus. Feel DifEq is like a breed of its own..aha

I know you have to use this type of an equation: VC = V0(1− e−t /τ ) where τ = RC and V0 is the initial voltage
 
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  • #2
anyone?
 
  • #3
I'm a little confused by your equations..

In general the voltage across a series RC circuit will decay exponentially, on a time constant determined by the value of RC.

The voltage across a resistor is:

[tex]V_R = IR = R\frac{dQ}{dt}[/tex]

The voltage across a capacitor is:

[tex]V_C = Q/C[/tex]

Knowing this, you should be able to set up a simple differential equation which will provide the answer you desire.
 

FAQ: Need help finding voltage across a capacitor in an RC circuit?

What is an RC circuit and how does it work?

An RC (resistor-capacitor) circuit is a type of electrical circuit that contains both a resistor and a capacitor. The resistor controls the flow of current and the capacitor stores electrical energy. When connected in series, the capacitor charges up to the same voltage as the battery or power source, and then slowly discharges as the current flows through the resistor.

What is the time constant of an RC circuit?

The time constant, denoted by the symbol τ, is a measure of how quickly a capacitor charges or discharges in an RC circuit. It is calculated by multiplying the resistance (R) in ohms by the capacitance (C) in farads, τ = RC. It represents the amount of time it takes for the capacitor to charge up to approximately 63% of its maximum voltage or discharge to 37% of its initial voltage.

How do I calculate the total resistance of a series RC circuit?

In a series RC circuit, the total resistance (RT) is equal to the sum of the resistance of the resistor (R) and the reactance of the capacitor (XC). The formula for calculating RT is: RT = R + XC, where XC = 1/(2πfC) and f is the frequency of the circuit in Hertz (Hz) and C is the capacitance in farads (F).

What is the phase relationship between voltage and current in an RC circuit?

In an RC circuit, the voltage and current are out of phase with each other. This means that they do not reach their maximum or minimum values at the same time. The voltage leads the current by 90 degrees in a charging circuit, and the current leads the voltage by 90 degrees in a discharging circuit. This phase difference is due to the time it takes for the capacitor to charge or discharge in response to the voltage.

How can I analyze and interpret the behavior of an RC circuit?

To analyze an RC circuit, you can use Kirchhoff's laws and the principles of Ohm's law. By applying these laws and equations, you can calculate the voltages and currents at different points in the circuit. You can also use circuit simulation software to model and visualize the behavior of an RC circuit. The behavior of an RC circuit depends on factors such as the values of the resistor and capacitor, the frequency of the circuit, and the initial voltage of the capacitor.

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