The specification on a heater coil is `250 V, 500 W`. Calculate the resistance of the coil. What will be the resistance of a coil of `1000W` to operate at the same voltage?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between power, voltage, and resistance
We know from the formula relating power (P), voltage (V), and resistance (R):
\[ P = \frac{V^2}{R} \]
From this, we can rearrange the formula to find resistance:
\[ R = \frac{V^2}{P} \]

### Step 2: Calculate the resistance of the 500 W heater coil
Given:
- Voltage (V) = 250 V
- Power (P) = 500 W

Now, substituting the values into the formula:
\[ R = \frac{(250)^2}{500} \]

### Step 3: Perform the calculation
Calculating \( (250)^2 \):
\[ (250)^2 = 62500 \]

Now substituting this value back into the equation:
\[ R = \frac{62500}{500} \]

Now, perform the division:
\[ R = 125 \, \Omega \]

### Step 4: Calculate the resistance of the 1000 W heater coil
Now we need to find the resistance for a heater coil rated at 1000 W, using the same voltage (250 V).

Given:
- Voltage (V) = 250 V
- Power (P) = 1000 W

Using the same formula:
\[ R = \frac{V^2}{P} \]

Substituting the values:
\[ R = \frac{(250)^2}{1000} \]

### Step 5: Perform the calculation
Again, we already know \( (250)^2 = 62500 \):
\[ R = \frac{62500}{1000} \]

Now, perform the division:
\[ R = 62.5 \, \Omega \]

### Final Results
- The resistance of the 500 W heater coil is **125 Ω**.
- The resistance of the 1000 W heater coil is **62.5 Ω**.

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