1. Let the resistance of each identical heater filament be $R$.

2. Case 1: Filaments connected in parallel

   Equivalent resistance: $R_p = \frac{R\cdot R}{R+R} = \frac{R}{2}$

   Heat produced in time $t$ at applied voltage $V$ is given by: $H = \frac{V^2}{R_{eq}}t$

   So, for parallel combination: $H_p = \frac{V^2}{R/2}t = \frac{2V^2 t}{R}$

3. Case 2: Filaments connected in series

   Equivalent resistance: $R_s = R + R = 2R$

   Heat produced in time $t$: $H_s = \frac{V^2}{2R}t$

4. Find the ratio of heat produced $\frac{H_p}{H_s} = \frac{\frac{2V^2 t}{R}}{\frac{V^2 t}{2R}}$

   $\frac{H_p}{H_s} = 4$

   Therefore, $H_p : H_s = 4:1$

5. Option check

   • A: $4:1$ ✅
   • B: $1:4$ ❌
   • C: $2:1$ ❌
   • D: $1:2$ ❌

So the correct answer is A.