Question

A heating element in a stove is designed to receive 4,430 W when connected to 240 V. (a) Assuming the resistance is constant, calculate the current in the heating element if it is connected to 120 V. Calculate the resistance and from it the current, using the given information about the power delivered. A (b) Calculate the power it receives at that voltage.

Answer 1

Answer:

a) The current in the heating element when it is connected to 120 V is 9.229 amperes, b) The power received by the heatng element connected to 120 V is 1107.522 watts.

Explanation:

a) The resistance as a function of voltage and power can be obtained from this expression, derived from the Ohm's Law:

$\dot W = \frac{V^{2}}{R}$

Where:

$V$ - Source voltage, measured in volts.

$R$ - Heating element resistance, measured in ohms.

Now, resistance is clear and determined afterwards:

$R = \frac{V^{2}}{\dot W}$

If $V = 240\,V$ and $\dot W = 4,430\,W$, then:

$R = \frac{(240\,V)^{2}}{4.430\,W}$

$R = 13.002\,\Omega$

Now, let consider that heating element is conected to a 120-V source. The power generated by this element is:

$\dot W = \frac{V^{2}}{R}$

$\dot W = \frac{(120\,V)^{2}}{13.002\,\Omega}$

$\dot W = 1107.522\,W$

Besides, power as a function of current and resistance is given by this:

$\dot W = i^{2}\cdot R$

Where $i$ is the current required by the heating element, measured in amperes, and which is cleared herein:

$i = \sqrt{\frac{\dot W}{R} }$

If $\dot W = 1107.522\,W$ and $R = 13.002\,\Omega$, then:

$i = \sqrt{\frac{1107.522\,W}{13.002\,\Omega} }$

$i \approx 9.229\,A$

The current in the heating element when it is connected to 120 V is 9.229 amperes.

b) The power received by the heatng element connected to 120 V is 1107.522 watts. (see point a) for further details)