Tutor profile: Tinsley B.

There is a node on a circuit with 2 currents coming in and 1 current exiting. a) If we know that one current into the node is $$i(1)=10 Amps$$ and the current leaving the node is $$i(3)=12$$ amps what is the other current entering the node $$i(2)=?$$. b) now that we found I(2), if the node has a voltage and I(2) runs across a 10 ohm resistor to ground what is the voltage at the node.

a) Here we apply Kirchoff's current law that all currents entering the node is equal to the currents exiting the node. $$10A+i(2)= 12A$$ $$i(2)=2A$$ b) Here we apply Ohm's Law $$\triangle(V)=I*R$$ $$(voltage @node-0)Volts=(2A)(10Ohms)$$ voltage at the node$$=20V$$

A resistor of 30 ohms is in series with a capacitor with an impedance of -j50 ohms and is also in series with an inductor with an impedance of j90 ohms. What is the total impedance, and which quadrant would the impedance vector lie in?

To find the total impedance, we add them together as follows: $$30+j90+(-j50)= 30 +j40$$ Therefore, our impedance vector would lie in quadrant 1.

A manufacturing company will purchase a large piece of equipment for $5,000. Annual maintenance will be $100. The buyback at the end of 5 years is $1,000. What is the annual cost of the equipment at $$i=12$$%?

Step 1 find the A/P (annual based on the present) at 12% for the $5,000. We can use the table or the formula. For this problem, I will show the formula. $$\frac{(i(1+i)^n)} {((1+i)^n-1)}$$ we know $$i=12$$% which would be 0.12 and we know that $$n=5$$years. So, plugging those values into the formula we obtain 0.277409. We multiply this number by $5,000 to get the $$annual purchase cost=$1387.05$$ Step 2. find the A/F for the buyback. (annual based on future). Note that since the buyback is not a cost, it will be a subtracted value at the end. But the process is the same as in step 1. However, for this step, we will use the interest tables. rather than the A/F formula. First, go to the correct interest table. ours is 12%. Second, go to the correct column. Ours is the A/F column. Last go to the correct row for the year. Ours is 5 years. The value we found is 0.1574. Multiply this value by the buyback worth of $1,000 to find the $$annual buyback worth=$157.4 $$ Step 3 Combine all 3. Note the annual cost for maintenance is already in terms of annual cost so no modifications needed to be made. $$annual cost=annual purchase cost+annual maintenance-annual buyback worth$$ $$1387.05+100-157.40=1329.65$$ $$annual cost =$1329.65$$