A 1250 W heater operates at `115V`. What is the resistance of the heating coil?

Options

A. `1.6Omega`
B. `13.5Omega`
C. `1250Omega`
D. `10.6Omega`

Answer

To find the resistance of the heating coil in a 1250 W heater operating at 115 V, we can use the formula that relates power (P), voltage (V), and resistance (R):

1. **Start with the formula for power:**
\[ P = \frac{V^2}{R} \]
Rearranging this formula to solve for resistance (R):
\[ R = \frac{V^2}{P} \]

2. **Substitute the given values into the formula:**
- Power (P) = 1250 W
- Voltage (V) = 115 V
\[ R = \frac{(115)^2}{1250} \]

3. **Calculate \(V^2\):**
\[ V^2 = 115^2 = 13225 \]

4. **Now substitute \(V^2\) back into the resistance formula:**
\[ R = \frac{13225}{1250} \]

5. **Perform the division:**
\[ R = 10.58 \, \text{ohms} \]

6. **Round the answer to two decimal places:**
\[ R \approx 10.6 \, \text{ohms} \]

Thus, the resistance of the heating coil is approximately **10.6 ohms**.