Question

the heating element of an electric oven is designed to produce 4.0 kw of heat when connected to a 240 - v source. part a what must be the resistance of the element? express your answer to two significant figures and include the appropriate units.

Explanation:

Step1: Recall the power formula

The power formula is \(P=\frac{V^{2}}{R}\), where \(P\) is power, \(V\) is voltage, and \(R\) is resistance. We need to solve for \(R\), so we can re - arrange the formula to \(R = \frac{V^{2}}{P}\).

Step2: Substitute the given values

Given \(V = 240\space V\) and \(P=4000\space W\) (since \(4.0\space kW = 4000\space W\)). Substitute these values into the formula \(R=\frac{(240)^{2}}{4000}\).
First, calculate \((240)^{2}=240\times240 = 57600\). Then, \(\frac{57600}{4000}=14.4\space\Omega\).

Answer:

\(14\space\Omega\)