A coil takes 15 min to boil a certain amount of water, another coil takes 20 min for the same process. Time taken to boil the same amount of water when both coil are connected in series

Options

A. (a)5 minutes
B. (b)8.6 minutes
C. (c)35 minutes
D. (d)30 minutes

Answer

To solve the problem, we need to determine the time taken to boil the same amount of water when both coils are connected in series. Let's break down the solution step by step:

### Step 1: Understand the relationship between power, resistance, and time
The power (P) generated by a coil is given by the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage applied and \( R \) is the resistance of the coil.

### Step 2: Analyze the time taken by each coil
From the problem, we know:
- Coil 1 takes 15 minutes to boil water.
- Coil 2 takes 20 minutes to boil the same amount of water.

The time taken (T) is inversely proportional to the power (P) of the coils. Therefore, we can express the relationship as:
\[ T \propto \frac{1}{P} \]

### Step 3: Determine the equivalent resistance when coils are in series
When the coils are connected in series, the total resistance \( R_{\text{eq}} \) is the sum of the individual resistances:
\[ R_{\text{eq}} = R_1 + R_2 \]

### Step 4: Establish the relationship between time and resistance
Since the time taken to boil water is directly proportional to the resistance, we can say:
\[ T_{\text{eq}} \propto R_{\text{eq}} \]

### Step 5: Calculate the equivalent time
Let’s denote the time taken by the first coil as \( T_1 = 15 \) minutes and by the second coil as \( T_2 = 20 \) minutes. The equivalent time when both coils are connected in series can be calculated as:
\[ T_{\text{eq}} = T_1 + T_2 = 15 + 20 = 35 \text{ minutes} \]

### Conclusion
Thus, the time taken to boil the same amount of water when both coils are connected in series is **35 minutes**.