In order to calculate the resistance of each appliance, we can use the formula below:
[tex]R=\frac{V^2}{P}^{}[/tex]
Where R is the resistance (in ohms), V is the voltage (in Volts) and P is the power (in Watts).
Since all appliances are in parallel, the voltage in each one is the same: 120 V.
So we have:
[tex]\begin{gathered} R_1=\frac{120^2}{80}=180\text{ ohms} \\ R_2=\frac{120^2}{250}=57.6\text{ ohms} \\ R_3=\frac{120^2}{440}=32.73\text{ ohms} \end{gathered}[/tex]
Resistances: R1 = 180 ohms, R2 = 57.6 ohms and R3 = 32.73 ohms.
Now, to find the readings of each ammeter, let's use the formula below:
[tex]\begin{gathered} I=\frac{P}{V} \\ I_1=\frac{80}{120}=0.667\text{ A} \\ I_2=\frac{250}{120}=2.083\text{ A} \\ I_3=\frac{440}{120}=3.667\text{ A} \\ I=I_1+I_2+I_3 \\ I=6.417\text{ A} \end{gathered}[/tex]
Therefore the measure of A is 6.417, A1 is 0.667, A2 is 2.083 and A3 is 3.667.
To find the total energy used in one hour, let's sum all the powers and multiply by 3600 seconds (that is, 1 hour):
[tex]\begin{gathered} E_{\text{electric}}=P\cdot t \\ E_{\text{electric}}=(80+250+440)\cdot3600 \\ E_{\text{electric}}=2772000\text{ J} \end{gathered}[/tex]
Total electrical energy used: 2,772,000 Joules.
