Answer:
1.61ohms and 4.39ohms
Explanation:
According to ohm's law which States that the current (I) passing through a metallic conductor at constant temperature is directly proportional to the potential difference (V) across its ends. Mathematically, E = IRt where;
E is the electromotive force
I is the current
Rt is the effective resistance
Let the resistances be R and r
When the resistors are connected in series to a 12.0-V battery and the current from the battery is 2.00 A, the equation becomes;
12 = 2(R+r)
Rt = R+r (connection in series)
6 = R+r ...(1)
If the resistors are connected in parallel to the battery and the total current from the battery is 10.2 A, the equation will become;
12 = 10.2(1/R+1/r)
Since 1/Rt = 1/R+1/r (parallel connection)
Rt = R×r/R+r
12 = 10.2(Rr/R+r)
12(R+r) = 10.2Rr ... (2)
Solving equation 1 and 2 simultaneously to get the resistances. From (1), R = 6-r...(3)
Substituting equation 3 into 2 we have;
12{(6-r)+r} = 10.2(6-r)r
12(6-r+r) = 10.2(6r-r²)
72 = 10.2(6r-r²)
36 = 5.1(6r-r²)
36 = 30.6r-5.1r²
5.1r²-30.6r +36 =
r = 30.6±√30.6²-4(5.1)(36)/2(5.1)
r = 30.6±√936.36-734.4/10.2
r = 30.6±√201.96/10.2
r = 30.6±14.2/10.2
r = 44.8/10.2 and r = 16.4/10.2
r = 4.39 and 1.61ohms
Since R+r = 6
R+1.61 = 6
R = 6-1.61
R = 4.39ohms
Therefore the resistances are 1.61ohms and 4.39ohms
Answer:
The answers to the question are as follows
The average speed of the aircraft = 112 miles/hr and
the average speed of the van= 57 miles/hr
Explanation:
Speed of the van = X
Speed of the aircraft = Y = 2 × X - 2 miles/hour
Distance covered by van in time t = 171 miles
Distance covered by aircraft in time t = 336 miles
Therefore Y × t = 336 miles and
X × t = 171 miles
Therefore (2·X -2) × t = 336 miles
and t = (171 miles)/X
(2·X -2) × (171 miles)/X = 336 miles
(342·X-342)/X =336 → 6·X = 342
Therefore X = 57 miles/hour
and Y =2×57 -2 = 112 miles/hr
Answer:
Centripetal acceleration of the car is 17.4 m/s²
Explanation:
It is given that,
Radius of the track, r = 57 m
Speed of car, v = 31.5 m/s
We need to find the centripetal acceleration of the race car. The formula for the centripetal acceleration is given by :
So, the centripetal acceleration of the race car is 17.4 m/s². Hence, this is the required solution.
Consider the reason that electric bulbs are manufactured in the first place: They are used to shed light on their world, to illuminate the darkness wherever they may be, to spread their warm reassuring glow for the benefit of all who may pass by.
An electric bulb uses a very thin wire, which heats to a high temperature and glows brightly when electric current passes through it. That wire is the strength of the electric bulb, but also its fatal weakness. For if the wire were surrounded by air when it heated and glowed, it would instantly burn up, and its glow would be extinguished forever. In order to keep the bulb glowing, air must not be allowed to reach it. This means that the wire must be sealed inside some sort of an enclosure that can be sealed so tight that even air cannot penetrate it.
The next question is: What to use for an air-tight enclosure ? It is said that Mr. Edison (the inventor of the electric light-bulb) tried more than 400 different ways to manufacture his invention, before he found one that was dependable enough to use in mass production. Edison himself claimed that the 400 failed experiments were trials of different materials for the filament ... the thin wire inside the bulb. But I suspect that many of those experiments involved the search for the best material to use to keep the air out, and prevent the thin wire from burning out. This relates exactly to the question you're asking.
I believe that Edison must have tried bulbs enclosed in steel, clay, salami, aluminum, stone, leather, wood, egg shell, cardboard, bone ... who knows what else. He eventually realized a critical related discovery: The enclosure for the fine wire not only needed to prevent air from entering the bulb, it also needed to allow light to get OUT ! I'm sure that as soon as this realization hit him, he rushed to his laboratory, tried a bulb surrounded by GLASS, and the rest became history.
