When Is the Potential Across a Capacitor Equal to That Across a Resistor?

In summary, the question asks at what time the potential across a capacitor, being charged through a resistor, is equal to the potential across the resistor. The circuit shown in Figure 27-63 can be solved using the equations v=vmax(1-e^-(t/RC)), V=iR, and i=imax(e^-(t/RC)). The answer is 0.208 ms. Attempts to solve using Ohm's law and the fact that the capacitor is fully charged when the current is zero were unsuccessful.
  • #1
Gabe805
17
0

Homework Statement


.
Switch http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math152.gif in Fig. 27-63 is closed at time http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/math/math164.gif, to begin charging an initially uncharged capacitor of capacitance 15 microfarads through a resistor of resistance 20 ohms. At what time is the potential across the capacitor equal to that across the resistor?
http://edugen.wileyplus.com/edugen/courses/crs7165/halliday9781118230725/c27/image_n/w1548-nn.png
Figure 27-63
Problems 57 and 96

Homework Equations


v=vmax(1-e^-(t/RC))
V=iR
i=imax(e^-(t/RC))[/B]

The Attempt at a Solution


The answer winds up being .208 ms. so I am just looking for an answer. I want to know how to solve this. I tried using ohms law to figure out what the voltage is across R but of course that was a dead end because the emf is not given. next I tried iR=vmax(1-e^-t/RC). Again a dead end. Also I know that when the capacitor is fully charged the current is zero, hence the voltage across R will also be zero but I couldn't figure out how to implement that knowledge into a solution. Any help would be greatly appreciated.[/B]
 

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  • #2
None of the links to your figures are working.
 
  • #3
I just uploaded another pic. In case that one doesn't work, the circuit is just an RC series circuit with a battery and a switch.
 

Related to When Is the Potential Across a Capacitor Equal to That Across a Resistor?

1. How does an RC circuit charge?

An RC circuit charges when a voltage source is connected to the circuit. The voltage source creates an electric field, which causes current to flow through the circuit. As the current flows, it charges the capacitor by storing energy in its electric field. This charging process continues until the capacitor reaches its maximum capacitance, at which point the current stops flowing and the capacitor is fully charged.

2. What is the time constant of an RC circuit?

The time constant of an RC circuit is a measure of how quickly the capacitor charges. It is calculated by multiplying the resistance (R) of the circuit by the capacitance (C) of the capacitor. The time constant is equal to the time it takes for the capacitor to charge to approximately 63% of its maximum capacitance.

3. How does the value of resistance affect the charging time of an RC circuit?

The value of resistance in an RC circuit affects the charging time by determining the rate at which current flows through the circuit. A higher resistance will result in a slower charging time, as it restricts the flow of current. Conversely, a lower resistance will result in a faster charging time.

4. What happens to the voltage and current in an RC circuit as the capacitor charges?

As the capacitor charges in an RC circuit, the voltage across the capacitor increases while the current flowing through the circuit decreases. This is because the capacitor is storing energy in its electric field, which reduces the amount of current flowing through the circuit. Once the capacitor is fully charged, the voltage across it will be equal to the voltage of the voltage source.

5. Can an RC circuit charge indefinitely?

No, an RC circuit cannot charge indefinitely. As the capacitor charges, the voltage across it increases while the current decreases. Eventually, the voltage across the capacitor will reach the same value as the voltage of the voltage source, and the current will stop flowing. This indicates that the capacitor is fully charged and cannot hold any more charge.

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