Answer:
R₁ = 50.77 Ω
Explanation:
Since, we know that:
Electric Power = P = VI
but from Ohm's Law:
V = IR
(or) I = V/R
Therefore,
P = V²/R
(OR) R = V²/P
where,
V = Battery Voltage
R = Resistance of combination
FOR SERIES COMBINATION:
R = Rs = (57 V)²/48 W
Rs = 67.69 Ω
but, we know that:
Rs = R₁ + R₂
R₁ + R₂ = 67.69 Ω
R₁ = 67.69 Ω - R₂ __________ eqn (1)
FOR PARALLEL COMBINATION:
R = Rp = (57 V)²/256 W
Rp = 12.69 Ω
but, we know that:
Rp = (R₁R₂)/(R₁ + R₂) = 12.69 Ω
using eqn (1) and value of R₁ + R₂, we get
Rp = 12.69 = R₂(67.69 - R₂)/67.69
859.08 = 67.69 R₂ - R₂²
R₂² - 67.69 R₂ + 859.08 = 0
Solving this quadratic equation we get the answers:
Either, R₂ = 50.76 Ω
Either, R₂ = 16.92 Ω
Since, it is stated in the question that R₁ > R₂. Therefore, we choose the second value. So,
<u>R₂ = 16.92 Ω</u>
using this value in eqn (1), we get:
R₁ = 67.69 Ω - 16.92 Ω
<u>R₁ = 50.77 Ω</u>
Answer:
567.321nm
Explanation:
See attached handwritten document for more details
Answer:

Explanation:
As we know that if the object is placed on the inclined plane then the force of friction on the object is counterbalanced by the component of the weight of the object along the inclined plane.
So we can say

now if we increase the inclination of the plane then the component of the weight weight along the inclined plane will increase and hence the friction force will also increase.
As we know that the limiting value or the maximum value of friction force at the static condition is given by


so we have

so we will have

so now we have

so maximum possible angle of the inclined plane is

Answer:
The velocity will be v = 22.1[m/s]
Explanation:
We can solve this problem by using the principle of energy conservation, where potential energy is converted to kinetic energy. For this problem we will take the point with maximum potential energy when the body is 25 [m] high. By the time the height is zero, the potential energy will have been transformed into kinetic energy, and we can find the velocity of the body.
![Ep = m*g*h\\where:\\m = mass = 88.2[kg]\\h = elevation = 25[m]\\g = gravity = 9.81 [m/s^2]\\Ep = 88.2*25*9.81 = 21631.05[J]\\](https://tex.z-dn.net/?f=Ep%20%3D%20m%2Ag%2Ah%5C%5Cwhere%3A%5C%5Cm%20%3D%20mass%20%3D%2088.2%5Bkg%5D%5C%5Ch%20%3D%20elevation%20%3D%2025%5Bm%5D%5C%5Cg%20%3D%20gravity%20%3D%209.81%20%5Bm%2Fs%5E2%5D%5C%5CEp%20%3D%2088.2%2A25%2A9.81%20%3D%2021631.05%5BJ%5D%5C%5C)
Now we know that the energy will be transformed.
![Ek=Ep\\Ek=0.5*m*v^{2} \\where:\\v=velocity [m/s]\\v=\sqrt{\frac{Ek}{0.5*m} } \\v=\sqrt{\frac{21631.05}{0.5*88.2} } \\v=22.14[m/s]](https://tex.z-dn.net/?f=Ek%3DEp%5C%5CEk%3D0.5%2Am%2Av%5E%7B2%7D%20%5C%5Cwhere%3A%5C%5Cv%3Dvelocity%20%5Bm%2Fs%5D%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7BEk%7D%7B0.5%2Am%7D%20%7D%20%5C%5Cv%3D%5Csqrt%7B%5Cfrac%7B21631.05%7D%7B0.5%2A88.2%7D%20%7D%20%5C%5Cv%3D22.14%5Bm%2Fs%5D)