How Is Voltage Across a Resistor Equivalent to That Across a Capacitor?

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SUMMARY

The discussion clarifies the equivalence of voltage across a resistor and a capacitor in a closed circuit. When the switch is closed and the capacitor is fully charged, the voltage across resistor R2 is equal to the voltage across the capacitor due to Kirchhoff's loop rule. This principle states that the net voltage change around any closed loop in a circuit must equal zero, confirming that the voltage difference between two points remains consistent across both components. Understanding this relationship is crucial for solving more complex circuit problems.

PREREQUISITES
  • Basic understanding of electrical circuits
  • Familiarity with Kirchhoff's loop rule
  • Knowledge of voltage, current, and resistance concepts
  • Experience with capacitors and their charging behavior
NEXT STEPS
  • Study Kirchhoff's laws in greater detail
  • Learn about capacitor charging and discharging equations
  • Explore series and parallel resistor configurations
  • Investigate the relationship between voltage, current, and resistance using Ohm's Law
USEFUL FOR

Students of electrical engineering, hobbyists working on circuit design, and anyone seeking to deepen their understanding of circuit analysis involving capacitors and resistors.

mcpoopants
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Alright, so there is a very basic theory involving capacitors and electric potential that is throwing me off. I have a very basic problem here: http://img444.imageshack.us/img444/2251/73619554.png

Assume the switch is closed and the capacitor is fully charged. From here I'm prompted to find the final voltage across the capacitor. Pretty obvious, you use V=IR, but I'm missing out on the value of "R". In this problem it is just R2, which is given to you. My problem is that I do not understand how the voltage across that resistor is equivalent to the voltage across that fully charged capacitor. It'd really help to explain as slowly as possible, because it is a basic idea that is kicking my butt in more complicated problems. Thanks to all.
 
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Use kirchhoffs loop rule around R2 and the capacitor. When you move from a point in a circuit, back to the same point, the net voltage change must be zero. This is the same thing as saying that the voltage difference between a point and itself is zero.

So, if a point on the top wire---between the resistor and capacitor---has a given voltage difference from a point on the bottom wire---between the resistor and cap---across the resistor, it has to be the same as across the capacitor... because they're the same two points.

Does that make any sense?
 

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