In a house, individual power of two elements are 10OW and 150 W . Effective power of their series combination will be

Options

A. 120W
B. 75W
C. 50W
D. 60W

Answer

To find the effective power of the series combination of two electrical elements with individual powers of 100 W and 150 W, we can follow these steps:

### Step 1: Identify the given values
Let:
- \( P_1 = 100 \, \text{W} \)
- \( P_2 = 150 \, \text{W} \)

### Step 2: Use the formula for effective power in series
The formula for the effective power \( P_{\text{effective}} \) of two elements in series is given by:

\[ \frac{1}{P_{\text{effective}}} = \frac{1}{P_1} + \frac{1}{P_2} \]

### Step 3: Substitute the values into the formula
Substituting the values of \( P_1 \) and \( P_2 \) into the formula:

\[ \frac{1}{P_{\text{effective}}} = \frac{1}{100} + \frac{1}{150} \]

### Step 4: Find a common denominator and simplify
To add the fractions, we need a common denominator. The least common multiple of 100 and 150 is 300. Therefore:

\[ \frac{1}{100} = \frac{3}{300}, \quad \frac{1}{150} = \frac{2}{300} \]

Now, add the fractions:

\[ \frac{1}{P_{\text{effective}}} = \frac{3}{300} + \frac{2}{300} = \frac{5}{300} \]

### Step 5: Take the reciprocal to find \( P_{\text{effective}} \)
Now, taking the reciprocal gives:

\[ P_{\text{effective}} = \frac{300}{5} = 60 \, \text{W} \]

### Conclusion
The effective power of the series combination of the two elements is \( 60 \, \text{W} \).

---