Answer:
Proof is as follows
Proof:
Given that , 
<u>for any function f with period T, RMS is given by</u>
<u />![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[f(t)]^{2} } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5Bf%28t%29%5D%5E%7B2%7D%20%7D%20%5C%2C%20dt%20%20%7D)
<u />
In our case, function is
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac} + V_{dc}]^{2} } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%20%2B%20V_%7Bdc%7D%5D%5E%7B2%7D%20%7D%20%5C%2C%20dt%20%20%7D)
Now open the square term as follows
![RMS = \sqrt{\frac{1}{T}\int\limits^T_0 {[V_{ac}^{2} + V_{dc}^{2} + 2V_{dc}V_{ac}] } \, dt }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7D%5Cint%5Climits%5ET_0%20%7B%5BV_%7Bac%7D%5E%7B2%7D%20%2B%20V_%7Bdc%7D%5E%7B2%7D%20%2B%202V_%7Bdc%7DV_%7Bac%7D%5D%20%7D%20%5C%2C%20dt%20%20%7D)
Rearranging terms
You can see that
- second term is square of RMS value of Vac
- Third terms is average of VdcVac and given is that average of
so
![RMS = \sqrt{\frac{1}{T}TV_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7BT%7DTV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
![RMS = \sqrt{V_{dc}^{2} + [RMS~~ of~~ V_{ac}]^2 }](https://tex.z-dn.net/?f=RMS%20%3D%20%5Csqrt%7BV_%7Bdc%7D%5E%7B2%7D%20%20%20%2B%20%5BRMS~~%20of~~%20V_%7Bac%7D%5D%5E2%20%7D)
So it has been proved that given expression for root mean square (RMS) is valid
Answer: The size of the ion and the charge of the ion are the factors that affect solubility in water.
Explanation:
Lead lose electrons to become cations. Compounds with small ions tend to be less soluble than compounds with large ions. Large ions have higher solubility. This is because small ions are closely packed so it is difficult for water to break them apart.
Compounds with small ions seemingly have less solubility than those with large ions. The ions in the compound attract each other, and the water molecules attract the ions. Compounds would be soluble in water If the water molecules have a greater or higher attraction to the ions than ions have for each other.
Answer:
61257.6 kW per day
Explanation:
The rating of the refrigerator is given as : 709 w
This means the power consumption is 709 joules per second
The operating time is given as 10 hours.
Change hours to second as
1 hour = 3600 seconds
10 hours = 36000 seconds
Apply the rating as;
709 w = 1 s
? = 36000 seconds
perform cross product to get;
709 * 36000= 25524000 w
25524000 = 25524kW
For a day, 24 hours will be;
25524 kW = 10 hours
? =24 hours
={24*25524}/10 = 61257.6 kW per day
Answer:
Technician B is correct.
Explanation:
Two technicians are discussing the a series-parallel brake lamp circuit that does not illuminate.
The statement made by Technician A saying that an open in one of the parallel branches could be the cause has no ground because an opening in any branches has not to do with the issue since there is no disconnection The statement made by Technician B saying that a shorted (or stuck closed) brake lamp switch wired in series could be the cause is correct.
