Derive the resistance value if power consumed by the heater is 32W and the potential difference is 16V?

Options

A. 12 ohm.
B. 30 ohm
C. 8 ohm
D. 55 ohm.

Explanation

To derive the resistance value when the power consumed by the heater is 32W and the potential difference is 16V, we can use the formula relating power, voltage, and resistance.

### Step-by-Step Solution:

1. **Understand the Power Formula**:
The power consumed by an electrical device can be expressed as:
\[ P = \frac{V^2}{R} \]
where \( P \) is the power in watts, \( V \) is the potential difference in volts, and \( R \) is the resistance in ohms.

2. **Rearrange the Formula to Solve for Resistance**:
We can rearrange the formula to find the resistance \( R \):
\[ R = \frac{V^2}{P} \]

3. **Substitute the Given Values**:
We know from the problem that:
- Power \( P = 32 \) W
- Voltage \( V = 16 \) V

Now substitute these values into the rearranged formula:
\[ R = \frac{16^2}{32} \]

4. **Calculate \( V^2 \)**:
First, calculate \( 16^2 \):
\[ 16^2 = 256 \]

5. **Calculate Resistance**:
Now substitute \( 256 \) back into the equation:
\[ R = \frac{256}{32} \]

6. **Perform the Division**:
Now divide \( 256 \) by \( 32 \):
\[ R = 8 \, \text{ohms} \]

### Final Answer:
The resistance value is \( 8 \, \text{ohms} \).

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