Heat Generation in a circuit due to moving charges

In summary, the problem involves finding the amount of heat generated inside a battery when a capacitor of capacitance C is charged by a battery of EMF E and internal resistance r with an additional resistance of 2r in series. The attempted solution involved using the equation q=Q(1-e-t/RC) and finding the time when the capacitor is 50% charged, but was unsuccessful due to the changing voltage and current requiring calculus. The hint given suggests using the integral of power with respect to time to find the energy. The suggested answer of E2/C is incorrect as it does not have the correct units for energy.
  • #1
deepak-
1
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1. Homework Statement
A capacitor of capacitance C id charged by a battery of emf E and inernal resistance r, A resistance 2r is also connected in series with the capacitor. The amount of heat liberated inside the battery by the time capacitor is 50% charged is? Answer is E2/C



2. Homework Equations
q=Q(1-e-t/RC)
btw, RC means the time constant and Q is the charge at steady state



3. The Attempt at a Solution
tried to find time when charge in capacitor is 50% charged and then find the heat using V2/R but had no success
 
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  • #2
The voltage and current are changing with time as the capacitor charges. This suggests that some calculus will be involved.

Hint: ∫ watts*dt = Energy
 
  • #3
You might also note that the answer suggested in the problem statement is clearly incorrect, as the units of E2/C are not energy.
 

FAQ: Heat Generation in a circuit due to moving charges

What is heat generation in a circuit due to moving charges?

Heat generation in a circuit is the process of converting electrical energy into thermal energy, which is caused by the movement of charges through the circuit. This occurs due to the resistance of the circuit components, which causes the electrons to collide with atoms and release energy in the form of heat.

How does heat affect the performance of a circuit?

Excessive heat can cause the components of a circuit to malfunction or even fail. This is because heat can cause changes in the physical properties of the materials used in the circuit, such as expansion or melting. It can also lead to an increase in resistance, which can affect the flow of current and ultimately the performance of the circuit.

How can heat generation be managed in a circuit?

Heat generation can be managed by using components with lower resistance, as this will reduce the amount of heat generated. Additionally, using heat sinks, fans, and other cooling methods can help dissipate the heat and prevent damage to the circuit. It is also important to ensure that the circuit is designed to handle the expected amount of heat generation.

What are some common causes of heat generation in a circuit?

One of the most common causes of heat generation in a circuit is current flow through a resistor, which converts electrical energy into heat energy. Other causes include poor connections, overloading the circuit, and using components that are not suitable for the amount of current passing through them.

How does heat generation impact the efficiency of a circuit?

Heat generation can reduce the efficiency of a circuit by converting some of the electrical energy into thermal energy instead of using it for the intended purpose. This can lead to energy loss and decrease the overall efficiency of the circuit. Managing heat generation is important to maintain the efficiency and performance of a circuit.

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