Thermal heat from a Capacitor

In summary, a resistor, capacitor, battery, and switch are connected in a circuit. The capacitor is charged from empty to full state. The energy stored in the capacitor is 66 \mu J and during charging, the work done by the battery is 72 \mu J. The energy emitted from the resistor is the difference between these values, resulting in 6 \mu J of thermal heat emitted. However, the unit check shows that the calculations may be incorrect. The correct equation for energy stored in the capacitor is E = C*Q^2.
  • #1
Horse
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0

Homework Statement



A resistor, a capacitor, a battery and a switch are connected to a circuit. The capacitor will be charged from the empty state to the full state.

During the period in which the capacitor is charged, how much thermal heat is emitted from the resistor?

[tex]C = 2 \mu F[/tex]
[tex]R = 2 \Omega[/tex]
[tex]E = 6 V[/tex]

Homework Equations



[tex]U = RI [/tex]
[tex]Q = CV[/tex]

The Attempt at a Solution



The amount of charge stored in the capacitor is: 6 V * 2 [tex]\mu F[/tex] = 12 [tex]\mu C [/tex].

The amount of work done by the battery is 12 [tex]\mu C [/tex]* 6 V *1/2 = 36 [tex]\mu J [/tex], during charging.

The amount of heat is (wrongly) 3/4 * 36 [tex] \mu J [/tex].
 
Last edited:
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  • #2
Horse said:

Homework Statement



A resistor, a capacitor, a battery and a switch are connected to a circuit. The capacitor will be charged from the empty state to the full state.

During the period in which the capacitor is charged, how much thermal heat is emitted from the resistor?

[tex]C = 2 \mu F[/tex]
[tex]R = 2 \Omega[/tex]
[tex]E = 6 V[/tex]

Homework Equations



[tex]U = RI [/tex]
[tex]Q = CV[/tex]

The Attempt at a Solution



The amount of charge stored in the capacitor is: 6 V * 2 [tex]\mu F[/tex] = 12 [tex]\mu C [/tex].

The amount of work done by the battery is 12 [tex]\mu C [/tex]* 6 V *1/2 = 36 [tex]\mu J [/tex], during charging.

The amount of heat is (wrongly) 3/4 * 36 [tex] \mu J [/tex].
What is the energy stored in the capacitor in terms of C and V?

Assume the energy stored in the capacitor is transformed into heat in the resistor when the capacitor discharges. How does this relate to the reverse when it charges?

AM
 
  • #3
Andrew Mason said:
What is the energy stored in the capacitor in terms of C and V?

Assume the energy stored in the capacitor is transformed into heat in the resistor when the capacitor discharges. How does this relate to the reverse when it charges?

AM

The energy (=QV) is 12 [tex]\mu C [/tex] * 6 V = 66 [tex]\mu J [/tex]. But somethig must be wrong, as I have:
Horse said:
The amount of work done by the battery is 12 [tex]\mu C [/tex]* 6 V *1/2 = 36 [tex]\mu J [/tex], during charging.

Perhaps, it is 12 [tex]\mu C [/tex]* 6 V = 72 [tex]\mu J [/tex]. ? Dunno why ?

If we suppose the logic right, we get a result for the energy emitted:

72 [tex]\mu J [/tex] - 66 [tex]\mu J [/tex] = 6 [tex]\mu J [/tex]

The amount of the thermal heat emitted is the difference between the energy emitted during discharging and the work done by the battery.

After-thought
NB. If I am right, the unit check shows that my calculations are wrong. E != CQ, E = C*Q^2. Now, I must be mistaken.
 
Last edited:

1. What is thermal heat from a capacitor?

Thermal heat from a capacitor is the heat generated as a result of the flow of electric current through a capacitor. This heat is a byproduct of the resistance and capacitance of the material used in the capacitor, and it can affect the performance and lifespan of the capacitor.

2. How does thermal heat affect a capacitor?

Excessive thermal heat can cause a capacitor to overheat, leading to a decrease in its capacitance and an increase in its internal resistance. This can result in circuit failures and damage to the capacitor, ultimately affecting the overall performance of the electronic device it is used in.

3. What factors can contribute to thermal heat in a capacitor?

The main factors that can contribute to thermal heat in a capacitor are the material used in its construction, the capacitance and voltage rating of the capacitor, and the amount of electric current flowing through it. Other factors like ambient temperature and surrounding components can also play a role.

4. How can thermal heat from a capacitor be managed?

To manage thermal heat from a capacitor, it is important to choose the right type and size of capacitor for the specific application. It is also important to consider the operating conditions and ensure proper ventilation and cooling. Additionally, using capacitors with lower internal resistance and higher voltage ratings can help reduce thermal heat.

5. What are the consequences of ignoring thermal heat in a capacitor?

Ignoring thermal heat in a capacitor can lead to premature failure of the capacitor and the electronic device it is used in. It can also cause malfunctioning of the circuit and potential safety hazards. It is important to carefully consider thermal heat when designing and using electronic devices to ensure optimal performance and longevity.

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