How Is Thermal Energy Produced in a Resistor During Capacitor Discharge?

[Daniiel]

I have a quick question.
part of one of my questions asks
"Find the rate at which thermal energy is produced in a resistor"
i havn't included the whole question because i don't think it matters, its just like the last part of it
so we have
http://edugen.wiley.com/edugen/courses/crs1650/art/math/halliday8019c27/math148.gif
thats the discharge of energy out of the capacitor
so
would the inverse of that be the rate at which the energy is moved into the resistor
like
1/u = 2ce/q (i left out a lot of things but thatsl ike the base of it)

orr
do you juts switch the e^- to e^+
because e^- is decay and e^+ is growth

yeh I am just abit confused which is right, or if either is right haha.
thanks

 

[kuruman]

I have a quick question.
part of one of my questions asks
"Find the rate at which thermal energy is produced in a resistor"
i havn't included the whole question because i don't think it matters,

It does matter. If the resistor is connected to the battery, thermal energy is constant with respect to time; if it is connected to a discharging capacitor (as seems to be the case here) then the thermal energy will be a function of time.

its just like the last part of it
so we have
http://edugen.wiley.com/edugen/courses/crs1650/art/math/halliday8019c27/math148.gif
thats the discharge of energy out of the capacitor

No. That's the energy stored in the capacitor at any time t.

so
would the inverse of that be the rate at which the energy is moved into the resistor
like
1/u = 2ce/q (i left out a lot of things but thatsl ike the base of it)

orr
do you juts switch the e^- to e^+
because e^- is decay and e^+ is growth

yeh I am just abit confused which is right, or if either is right haha.
thanks

None of the above. The rate at which energy is dissipated in the resistor (i.e. power dissipated) is given by
P = i²R, where i is the current in the resistor at a given time t. That's what you need to find an expression for.

 

[Daniiel]

what about
P(t)= V(t) I(t)
is that alright aswell?

 

[kuruman]

Yes it is, but you will have to find two functions of time, V(t) and I(t). If you use P = I²R, you will need only I(t).

 

[rdl]

The rate at which thermal energy is produced in a resistor can be calculated using the equation P = I^2R, where P is the power (rate of energy production), I is the current flowing through the resistor, and R is the resistance of the resistor. In the context of the discharge of a capacitor, the current through the resistor is related to the rate at which energy is moved into the resistor. The inverse of the discharge rate of the capacitor would not necessarily be the same as the rate at which energy is moved into the resistor, as the discharge rate also depends on the capacitance and charge of the capacitor. It is important to consider all relevant variables and equations when calculating the rate of thermal energy production in a resistor. Switching the e^- to e^+ may not be applicable in this situation, as it depends on the specific context and equations being used. It is important to carefully consider and understand the equations and variables involved in order to accurately calculate the rate of thermal energy production in a resistor.