Question

On a heater coil it is written \(250\,V, 500\,W\). What is the resistance of this coil?

• A. \(62.5\,\Omega\)
• B. \(100\,\Omega\)
• C. \(200\,\Omega\)
• D. \(125\,\Omega\)

Hint:

Use \( R = \frac{V^2}{P} \) when voltage and power are given.

Answer 1

The Correct Option is D

To find the resistance of the heater coil, we can use the relationship between power, voltage, and resistance. The formula that relates these quantities is given by:

\[ P = \frac{V^2}{R} \]

Where:

• \(P\) is the power in watts (W),
• \(V\) is the voltage in volts (V),
• \(R\) is the resistance in ohms (\(\Omega\)).

We are given the power \(P = 500\,W\) and the voltage \(V = 250\,V\). We need to find the resistance \(R\).

Rearrange the formula to solve for resistance:

\[ R = \frac{V^2}{P} \]

Substitute the given values:

\[ R = \frac{(250)^2}{500} \]

Calculate \(V^2\):

\[ 250^2 = 62500 \]

Now substitute back into the formula:

\[ R = \frac{62500}{500} = 125\,\Omega \]

Thus, the resistance of the coil is \(125\,\Omega\). This matches the given correct answer.