A metal rod consumes power P on passing curreent . If it is cut into two half and joined in parallel, it will consume power

Options

A. P
B. 2P
C. 4P
D. p/4

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial power consumption
The power consumed by the metal rod when it has a resistance \( R \) is given by the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage across the rod.

### Step 2: Determine the resistance of the cut rod
When the metal rod is cut into two equal halves, the resistance of each half becomes:
\[ R_1 = R_2 = \frac{R}{2} \]

### Step 3: Calculate the total resistance in parallel
When these two halves are joined in parallel, the equivalent resistance \( R_{eq} \) can be calculated using the formula for resistors in parallel:
\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Substituting the values of \( R_1 \) and \( R_2 \):
\[ \frac{1}{R_{eq}} = \frac{1}{\frac{R}{2}} + \frac{1}{\frac{R}{2}} = \frac{2}{R/2} = \frac{4}{R} \]
Thus, the equivalent resistance is:
\[ R_{eq} = \frac{R}{4} \]

### Step 4: Calculate the new power consumption
Now, we can find the power consumed by the two halves when connected in parallel using the power formula:
\[ P_{new} = \frac{V^2}{R_{eq}} = \frac{V^2}{\frac{R}{4}} = \frac{4V^2}{R} \]

### Step 5: Relate the new power to the original power
From the original power formula \( P = \frac{V^2}{R} \), we can substitute \( \frac{V^2}{R} \) with \( P \):
\[ P_{new} = 4 \left( \frac{V^2}{R} \right) = 4P \]

### Conclusion
Therefore, when the metal rod is cut into two halves and joined in parallel, it will consume power \( 4P \).

### Final Answer
The power consumed when the rod is cut and joined in parallel is \( 4P \).

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