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?

Explanation

To solve the problem of heat generated in a coil of resistance \( R \) due to a charge \( q \) passing through it under two different current decay scenarios, we can break it down into two parts:

### Part (a): Uniformly Decreasing Current

1. **Define the Current Decay**:
The current decreases uniformly from an initial value \( I_0 \) to 0 over a time interval \( t_0 \). The equation of the current as a function of time \( t \) can be expressed as:
\[
I(t) = I_0 \left(1 - \frac{t}{t_0}\right), \quad \text{for } 0 \leq t \leq t_0
...