What amount of heat will be generated in a coil resistance `R` due to a charge `q` passing through it if the current in the coil decreases down to zero uniformly during a time interval `Deltat` ?

Options

A. `(4)/(3)(q^(2)R)/(Deltat)`
B. `(2)/(3)(q^(2)R)/(Deltat)`
C. `(3)/(4)(q^(2)R)/(Deltat)`
D. `(3)/(2)(q^(2)R)/(Deltat)`

Explanation

To find the amount of heat generated in a coil of resistance \( R \) due to a charge \( q \) passing through it while the current decreases uniformly to zero over a time interval \( \Delta t \), we can follow these steps:

### Step 1: Understand the Current-Time Relationship
The current \( I \) decreases uniformly from an initial value \( I_0 \) to zero over the time interval \( \Delta t \). The current can be expressed as:
\[ I(t) = I_0 \left(1 - \frac{t}{\Delta t}\right) \]
for \( 0 \leq t \leq \Delta t \).
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