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What amount of heat will be generated in...

What amount of heat will be generated in a coil of resistance `R` due to a charge q passing through it if the current in the coil
a. decreases down to zero uniformly during a time interval `t_0`?
b. exponentially decrases down to zero having its value every `t_0` seconds?

A

`4/3 (q^2R)/T`

B

`1 n ((q^2R)/(2T))`

C

`(2q^2R)/(3T)`

D

`1 n ((2T)/(q^2R))`

Text Solution

Verified by Experts

The correct Answer is:
A
a. `I = I_0 - kt, "at" t = T, I = 0 or k = I_0//T`
So `I = I_0-I_0t//T, q = int_(0)^(T) Idt = I_(0) int_(0)^(T) (1- t/T) dt`
or `q = (I_0T)/2 or I_0 = (2q)/T`
Heat = `int_(0)^(T) I^(2) Rdt = I_(0)^(2)R int_(0)^(T) (1-t/T)^2 dt = (4q^2R)/(3T)` .
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