Time constants, resistance and RC circuits

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The time constant in an RC circuit indicates how quickly a capacitor can charge or discharge, with its value determined by the product of resistance and capacitance (R*C). As resistance increases, the time constant also increases, meaning the charging and discharging processes slow down, similar to how a smaller hose restricts water flow. This principle applies to both direct and alternating currents, although alternating currents are often discussed in terms of frequency. A time constant of 4.6 times R*C indicates that a capacitor is approximately 99% charged. Understanding these relationships is crucial for analyzing the behavior of RC circuits in various applications.
t_n_p
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I just need some help understanding some of the theory behind these..

Can anybody help explain the relevance of a time constant in an RC circuit and why the time constant increases as resistance increases?

Thanks in advance:blushing:
 
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Well, generally time constants will tell you how fast an inductor or capacitor can be energized or de-energized. If we talk about just capacitors, its how fast they can be charged or discharged. Since resistance tends to choke off current like a small hose vs a big one when filling or emptying a watertank, things get slower with increasing resistance generally. The same principles apply to alternating currents as well as to direct current, but there we usually talk about frequencies instead of a time constant.
 
t_n_p, the time constant in an RC circuit is usually R*C... so it is proportional to the first power of the resistance and the capacitance: if you were to put in a 2 Ohm resistor instead of a 1 ohm resistor, the time constant would be doubled. Usually, 4.6 * R*C means a capacitor which is 99% charged, so with the time constant you can more or less figure out how long a capacitor will take to charge to a certain percentage.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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