An electric heating element consumes 500 W when connected to a 100 V line. If the line voltage becomes 150 V, the power consumed will be

Options

A. 500 W
B. 750 W
C. 1000 W
D. 1125 W

Explanation

To solve the problem step by step, we will use the relationship between power, voltage, and resistance.

### Step 1: Identify the given values
- Power consumed at 100 V, \( P_1 = 500 \, W \)
- Voltage at which this power is consumed, \( V_1 = 100 \, V \)
- New voltage, \( V_2 = 150 \, V \)

### Step 2: Use the power formula
The power consumed by an electrical device is given by the formula:
\[ P = \frac{V^2}{R} \]
Where:
- \( P \) is the power,
- \( V \) is the voltage,
- \( R \) is the resistance.

### Step 3: Find the resistance using the first set of values
From the first condition (100 V and 500 W), we can express the resistance \( R \):
\[ P_1 = \frac{V_1^2}{R} \implies R = \frac{V_1^2}{P_1} \]
Substituting the known values:
\[ R = \frac{(100)^2}{500} = \frac{10000}{500} = 20 \, \Omega \]

### Step 4: Calculate the power at the new voltage
Now, we will find the power consumed at the new voltage \( V_2 = 150 \, V \):
\[ P_2 = \frac{V_2^2}{R} \]
Substituting the values of \( V_2 \) and \( R \):
\[ P_2 = \frac{(150)^2}{20} = \frac{22500}{20} = 1125 \, W \]

### Final Answer
The power consumed when the line voltage becomes 150 V is \( 1125 \, W \).

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