Time required to fully discharge the capacitor where did i go wrong?

In summary, a cube of gold with specific properties is connected to a capacitor with a certain potential difference. The resistance and capacitance values are used to calculate the time required for the capacitor to fully discharge, which is approximately 2.56 x 10-9 seconds. The units for the resistance should be Ohms, and it is possible that the marker may require a different unit for the result.
  • #1
yjk91
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0

Homework Statement



A cube of gold (resistivity ρR = 2.44 10-8 Ω m, density ρD = 1.93 104 kg / m3, and specific heat c = 129 J / kg °C) that is 3.5 mm on a side is connected across the terminals of a 40-µF capacitor that initially has a potential difference of 340.0 V between its plates.

http://www.webassign.net/bauerphys1/26-p-052.gif

What time is required to fully discharge the capacitor? (Assume the capacitor is fully discharged when the charge is less than 0.01%.)






The Attempt at a Solution




R = pL / A = (2.44 * 10^-8) * (3.5 * 10^-3m) / (3.5*10^-3m)^2 = 6.97 * 10^-6 m^2

C = 40 * 10^-6 F

Q = Q0 e (-t/(RC))

so

t = 2.56 e -9

which is not the right answer for question a
 
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  • #2
Your units for the resistance of the gold block should be Ohms, not square meters :smile:

I can't find a fault with your calculation (although the result when I calculated it rounded to 2.57 x 10-9 seconds).

Does the marker require any particular units to be used for the result (picoseconds? nanoseconds?)
 

1. How long does it take for a capacitor to fully discharge?

The time required for a capacitor to fully discharge depends on its capacitance, the voltage across it, and the resistance in the circuit. A larger capacitance, lower voltage, and higher resistance will result in a longer discharge time.

2. What is the formula for calculating the discharge time of a capacitor?

The formula for calculating the discharge time of a capacitor is t = RC, where t is the discharge time in seconds, R is the resistance in ohms, and C is the capacitance in farads. This assumes a simple RC circuit with no additional components.

3. Can the discharge time of a capacitor be shortened?

Yes, the discharge time of a capacitor can be shortened by decreasing its capacitance or increasing the resistance in the circuit. Additionally, using a circuit with additional components such as a diode or transistor can also shorten the discharge time.

4. How does temperature affect the discharge time of a capacitor?

Temperature can affect the discharge time of a capacitor by changing its capacitance and resistance. Higher temperatures can lead to a decrease in capacitance and an increase in resistance, resulting in a shorter discharge time. However, this effect is typically very small and may not be noticeable in most circuits.

5. Why is the discharge time of a capacitor important to consider?

The discharge time of a capacitor is important to consider because it can impact the performance and functionality of electronic circuits. If the discharge time is too long, it can affect the timing and accuracy of the circuit. Additionally, knowing the discharge time can help in the design and troubleshooting of circuits.

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