Question

determine the reading of  each ammeter, the resistance of each appliance, the total resistance of the ckt.  Calculate the total electrical energy(joules) used if all of the appliances are on for 1 hour

Answer 1

In order to calculate the resistance of each appliance, we can use the formula below:

`R=(V^2)/(P)^{}`

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:

`\begin{gathered} R_1=(120^2)/(80)=180\text{ ohms} \\ R_2=(120^2)/(250)=57.6\text{ ohms} \\ R_3=(120^2)/(440)=32.73\text{ ohms} \end{gathered}`

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:

`\begin{gathered} I=(P)/(V) \\ I_1=(80)/(120)=0.667\text{ A} \\ I_2=(250)/(120)=2.083\text{ A} \\ I_3=(440)/(120)=3.667\text{ A} \\ I=I_1+I_2+I_3 \\ I=6.417\text{ A} \end{gathered}`

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):

`\begin{gathered} E_{\text{electric}}=P\cdot t \\ E_{\text{electric}}=(80+250+440)\cdot3600 \\ E_{\text{electric}}=2772000\text{ J} \end{gathered}`

Total electrical energy used: 2,772,000 Joules.