1. Relevant formula for heat dissipated

   The heat dissipated in a resistor is given by Joule’s law: $H = I^2 R t$ where:

   • $I$ = current
   • $R$ = resistance
   • $t$ = time

2. Rule for maximum percentage error

   For a quantity of the form $Q = A^m B^n C^p$ the maximum fractional error is $\frac{\Delta Q}{Q} = m\frac{\Delta A}{A} + n\frac{\Delta B}{B} + p\frac{\Delta C}{C}$

   Applying this to $H = I^2Rt$ we get $\frac{\Delta H}{H} = 2\frac{\Delta I}{I} + \frac{\Delta R}{R} + \frac{\Delta t}{t}$

3. Substitute the given percentage errors

   Given: $\frac{\Delta R}{R} = 1\%,$ $\frac{\Delta I}{I} = 2\%,$ $\frac{\Delta t}{t} = 3\%$

   Therefore, $\frac{\Delta H}{H} = 2(2\%) + 1\% + 3\%$ $= 4\% + 1\% + 3\%$ $= 8\%$

4. Final answer

   The maximum percentage error in heat dissipated is: $\boxed{8\%}$

5. Option check

   • A: $2$ ❌
   • B: $4$ ❌
   • C: $6$ ❌
   • D: $8$ ✅

So the correct option is D.