A heater coil is rated 100W,200V. It is cut into two identical parts. Both parts are connected together in parallel, to the same sources of 200V. Calculate the energy liberated per second in the new combination.

Options

A. 100J
B. 200J
C. 300J
D. 400J

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Initial Conditions
The heater coil is rated at 100W and 200V. This means that under normal operation, the heater uses 100 watts of power when connected to a 200-volt supply.

### Step 2: Calculate the Resistance of the Original Heater Coil
Using the formula for power:
\[ P = \frac{V^2}{R} \]
We can rearrange it to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]
Substituting the values:
\[ R = \frac{200^2}{100} = \frac{40000}{100} = 400 \, \Omega \]
So, the resistance of the original heater coil is 400 ohms.

### Step 3: Determine the Resistance of Each Cut Part
Since the coil is cut into two identical parts, the resistance of each part will be half of the original resistance:
\[ R_{\text{each}} = \frac{R}{2} = \frac{400}{2} = 200 \, \Omega \]
Thus, each part has a resistance of 200 ohms.

### Step 4: Calculate the Equivalent Resistance of the Parallel Combination
When two resistors are connected in parallel, the equivalent resistance \( R' \) can be calculated using the formula:
\[ \frac{1}{R'} = \frac{1}{R_1} + \frac{1}{R_2} \]
Since both resistors are equal:
\[ \frac{1}{R'} = \frac{1}{200} + \frac{1}{200} = \frac{2}{200} = \frac{1}{100} \]
Thus, the equivalent resistance is:
\[ R' = 100 \, \Omega \]

### Step 5: Calculate the Power in the New Combination
Now that we have the equivalent resistance, we can calculate the power (energy liberated per second) using the formula:
\[ P = \frac{V^2}{R'} \]
Substituting the values:
\[ P = \frac{200^2}{100} = \frac{40000}{100} = 400 \, W \]
Therefore, the energy liberated per second in the new combination is 400 watts.

### Final Answer
The energy liberated per second in the new combination is **400 joules**.

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