For a given voltage V, if resistance is changed from R to `(R/n)` power consumed changes from P to

Options

A. `np`
B. `(P)/(n )`
C. `n^2 p`
D. `(P )/(n^2)`

Explanation

To solve the problem, we need to determine how the power consumed changes when the resistance is altered from \( R \) to \( \frac{R}{n} \) while keeping the voltage \( V \) constant.

### Step-by-step Solution:

1. **Understand the Power Formula**:
The power \( P \) consumed in an electrical circuit can be expressed using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage and \( R \) is the resistance.

2. **Calculate Initial Power**:
For the initial resistance \( R \), the power \( P_1 \) can be calculated as:
\[ P_1 = \frac{V^2}{R} \]

3. **Calculate New Power with Changed Resistance**:
When the resistance is changed to \( \frac{R}{n} \), the new power \( P_2 \) can be calculated as:
\[ P_2 = \frac{V^2}{\frac{R}{n}} = \frac{V^2 \cdot n}{R} \]

4. **Relate the New Power to the Initial Power**:
We can express \( P_2 \) in terms of \( P_1 \):
\[ P_2 = n \cdot \frac{V^2}{R} = n \cdot P_1 \]
Since \( P_1 = \frac{V^2}{R} \), substituting gives:
\[ P_2 = n \cdot P_1 \]

5. **Final Result**:
Therefore, if the resistance is changed from \( R \) to \( \frac{R}{n} \), the power consumed changes from \( P \) to \( nP \).

### Conclusion:
The power consumed changes from \( P \) to \( nP \).

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