Question

suppose we have two sinusoidal voltages of the same frequency with rms values of 10v and 7v, respectively. The phase angles are unknown. What is the smallest rms value that the sum of these voltages could have? The largest? Justify your answers.

Answer 1

this question is easy just that i don't see why the logic...

Answer 2

shouldn't it be 17v and -17v. Not 17v and 3v?

Answer 3

Its an electrical engineering question in case you don't know. But still maths....all the same

Answer 4

you guys all fail lol

Answer 5

smalest i gues would be 0, largest = 17

Answer 6

ah k well your wrong. its 17v and 3v. but i don't see the logic

Answer 7

remind me what rms is exactly

Answer 8

root mean square

Answer 9

ok, its preaty easy...

Answer 10

yeh it is really easy but the logic can go multiple ways

Answer 11

check this:
http://www.nuffieldfoundation.org/practical-physics/explaining-rms-voltage-and-current

Answer 12

other way to see it is: think of rms as equivalent constant voltage that produce same work. To find the max, min value of difference just take the abolute value of a diference of this constant voltages

Answer 13

min absolute value of difference is 3
max 17

Answer 14

ok so the answer cannot be negative because it is divided by root 2

Answer 15

not becouse of that

Answer 16

rms is always positive

Answer 17

because its absolute value

Answer 18

yeh and that...i see...i was just thinking if its possible that one sinusoidal is negative they can be negative lol...i was wrong again

Answer 19

*both

Answer 20

you just thinking, that's good way to learn :)

Answer 21

If they were both "exactly" the same frequency and remained exactly the same frequency their rms sum would depend on their initial phase difference which would remain the same provided they remained "on frequency" The resultant would be a constant rms value, but could be, depending on the initial phase difference anywhere from 3 to 17 volts rms as you have stated..