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2.7A 110 V heating element in a stove can boil a standard-size pot of water in 1.2 minutes, consuming a total of 136 kJof energy. Determine the resistance of the heating element andthe current flowing through it.

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gennerandrescarrillo

Answer:

Resistance of the heating element: 6.4 ohm

Current flow:17.17 amperes

Explanation:

First we need to convert from Joules to Watts, in order to do that we need the time in seconds:

[tex]1.2 minutes= 1.2mins \frac{60 seconds}{1 minute} = 72 seconds[/tex]

Then apply the formula:

[tex]E(J)= Watts* t(seconds)\\136000= Watts* 72 seconds[/tex]

Clearing watts from the equation:

[tex]watts=\frac{136000}{72} = 1888.9 w[/tex]

Then, we know the input voltaje is 110V, and Watts= Voltage* Current.

[tex]\frac{Watts}{Voltage} =Current\\\\current=\frac{1888.9}{110} =17.17 amp[/tex]

Finally Voltaje over Current= Resistance, from ohm's law

[tex]\frac{V}{I} =r=\frac{110}{17.17} = 6.4 ohms[/tex]

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