# eletric current-heat produced in varying charge situation

in a circuit there are two resistances each R in series Across any one R there is resistance 2R in parallel The arrangement is connected to a source The charge supplied by source varies with time t as Q=at-bt^2 what is the total heat produced in resistor 2R

• Lokesh Verma ·

More details are needed in this quesiton because you have not specified the starting and end time.
Even if the starting time is 0. the ending time is not specified.

I will give an outline on how ths can be done assuming that u have taken Q
Q=at-bt^2
=> I= a-2bt
so the time when I becomes zero is t=a/2b
If we try to solve this problem for this condition, look into the next section of this question.

• Lokesh Verma ·

Continuing,

We get I (t) in the previous part as the derivative of Q.

if current I passes thru the wire or Resistance '2R' will be R*I/(2R+R)
so the current passing thru 2R will be I/3
so heat generation rate I^R
but we will have to integrate this value from initial to end point.
This method should be used to reach the final answer.

I hope this helps you solve the problem :)

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