A resistor of resistance R is connected to a cell internal resistance `5 Omega`. The value of R is varied from ` 1 Omega` to `5 Omega`. The power consumed by R

Options

A. increases continuously
B. decreases continuously
C. first decreases then increases
D. first increases then decreases

Answer

To solve the problem of finding the power consumed by a resistor \( R \) connected to a cell with an internal resistance of \( 5 \, \Omega \), we will follow these steps:

### Step 1: Understand the Circuit
The total resistance in the circuit is the sum of the external resistance \( R \) and the internal resistance of the cell, which is \( 5 \, \Omega \). Therefore, the total resistance \( R_{total} \) can be expressed as:
\[ R_{total} = R + 5 \, \Omega \]

### Step 2: Apply Ohm's Law
According to Ohm's Law, the current \( I \) flowing through the circuit can be calculated using the formula:
\[ I = \frac{V}{R_{total}} \]
where \( V \) is the voltage of the cell.

### Step 3: Substitute Total Resistance
Substituting the expression for \( R_{total} \) into the current equation, we get:
\[ I = \frac{V}{R + 5} \]

### Step 4: Calculate Power
The power \( P \) consumed by the resistor \( R \) can be calculated using the formula:
\[ P = I^2 R \]
Substituting the expression for \( I \) from Step 3:
\[ P = \left( \frac{V}{R + 5} \right)^2 R \]
This simplifies to:
\[ P = \frac{V^2 R}{(R + 5)^2} \]

### Step 5: Analyze Power Variation
Now, we need to analyze how the power \( P \) changes as \( R \) varies from \( 1 \, \Omega \) to \( 5 \, \Omega \). Since \( P \) is a function of \( R \):
\[ P(R) = \frac{V^2 R}{(R + 5)^2} \]
We can observe that as \( R \) increases, the numerator \( V^2 R \) increases, while the denominator \( (R + 5)^2 \) also increases but at a slower rate initially.

### Step 6: Conclusion
To conclude, as \( R \) increases from \( 1 \, \Omega \) to \( 5 \, \Omega \), the power consumed by the resistor \( R \) will also increase continuously. Thus, the answer to the question is that the power consumed by \( R \) increases continuously as \( R \) varies from \( 1 \, \Omega \) to \( 5 \, \Omega \).