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Simora [160]
3 years ago
6

Three identical resistors are connected in parallel. The equivalent resistance increases by 630 when one resistor is removed and

connected in series with the remaining two, which are still in parallel. Find the resistance of each resistor.
Physics
1 answer:
strojnjashka [21]3 years ago
8 0

Answer:

each resistor is 540 Ω

Explanation:

Let's assign the letter R to the resistance of the three resistors involved in this problem. So, to start with, the three resistors are placed in parallel, which results in an equivalent resistance R_e defined by the formula:

\frac{1}{R_e}=\frac{1}{R} } +\frac{1}{R} } +\frac{1}{R} \\\frac{1}{R_e}=\frac{3}{R} \\R_e=\frac{R}{3}

Therefore, R/3 is the equivalent resistance of the initial circuit.

In the second circuit, two of the resistors are in parallel, so they are equivalent to:

\frac{1}{R'_e}=\frac{1}{R} +\frac{1}{R}\\\frac{1}{R'_e}=\frac{2}{R} \\R'_e=\frac{R}{2} \\

and when this is combined with the third resistor in series, the equivalent resistance (R''_e) of this new circuit becomes the addition of the above calculated resistance plus the resistor R (because these are connected in series):

R''_e=R'_e+R\\R''_e=\frac{R}{2} +R\\R''_e=\frac{3R}{2}

The problem states that the difference between the equivalent resistances in both circuits is given by:

R''_e=R_e+630 \,\Omega

so, we can replace our found values for the equivalent resistors (which are both in terms of R) and solve for R in this last equation:

\frac{3R}{2} =\frac{R}{3} +630\,\Omega\\\frac{3R}{2} -\frac{R}{3} = 630\,\Omega\\\frac{7R}{6} = 630\,\Omega\\\\R=\frac{6}{7} *630\,\Omega\\R=540\,\Omega

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Talja [164]

(A) For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system.

(D) For the system consisting of the two blocks, the pulley and the Earth, the change in the total mechanical energy of the system is zero.

<h3 /><h3>The given parameters:</h3>
  • Mass of block 1 = m1
  • Mass of block 2, = m2
  • Height of block 1 above the ground, = h1
  • Height of block 2 above the ground = h2

The total initial mechanical energy of the two block system is calculated as follows;

m_1gh_1 + \frac{1}{2} m_1v_1_i^2 = m_2gh_2 + \frac{1}{2} m_2v_2_i^2\\\\m_1gh_1 + 0 = m_2gh_2 + 0\\\\m_1gh_1 = m_2gh_2\\\\m_1gh_1 - m_2gh_2 = 0

When the block m2 reaches the ground the block m1 attains maximum height and the total mechanical energy at this point is given as;

m_1g(h_1 + h_2) + K.E_1 = \frac{1}{2}m_2v_{max}^2 + P.E_2\\\\m_1g(h_1 + h_2 ) -PE_2 = \frac{1}{2}m_2v_{max}^2 - K.E_1\\\\m_1g(h_1 + h_2 )  - 0= \frac{1}{2}m_2v_{max}^2 - 0\\\\m_1g(h_1 + h_2 )  = \frac{1}{2}m_2v_{max}^2\\\\W = \frac{1}{2}m_2v_{max}^2

Thus, we can conclude the following before the block m2 reaches the ground;

  • For the system consisting of the two blocks, the pulley and the Earth, the change in the total mechanical energy of the system is zero.
  • For the system consisting of the two blocks, the change in the kinetic energy of the system is equal to work done by gravity on the system.

Learn more about conservation of mechanical energy here: brainly.com/question/332163

5 0
3 years ago
2. A liquid that is twice as dense as water is used in a barometer. With this barometer, atmospheric pressure would push the liq
Scrat [10]

Answer:

The reason why the height for the liquid is 5.18 m is because, for constant pressure, height is inversely proportional to density.

Explanation:

We know that pressure, P = ρgh where ρ = density of material, g = 9.8 m/s and h = height.

Since density of liquid = 2 × density of water = 2 × 1000 kg/m = 2000 kg/m³

Since atmospheric pressure = 101500 N/m²,

The height of liquid for this pressure is h = P/ρg = 101500/(2000 × 9.8) = 5.18 m

For the same pressure, the height for water is h = P/ρg = 101500/(1000 × 9.8) = 10.36 m

Since pressure = constant,

P = ρgh ⇒ P/ρg = h since P and g are constant, h ∝ 1/ρ

ρ₁h₁ = ρ₂h₂

So, the reason why the height for the liquid is 5.18 m is because, for constant pressure, height is inversely proportional to density.

8 0
3 years ago
How can I solve this?
inysia [295]
There is no equation here
3 0
3 years ago
When water freezes, its volume increases by 9.05% (that is, equation). What force per unit area is water capable of exerting on
PIT_PIT [208]

Answer:

1.991 × 10^(8) N/m²

Explanation:

We are told that its volume increases by 9.05%.

Thus; (ΔV/V_o) = 9.05% = 0.0905

To find the force per unit area which is also pressure, we will use bulk modulus formula;

B = Δp(V_o/ΔV)

Making Δp the subject gives;

Δp = B(ΔV/V_o)

Now, B is bulk modulus of water with a value of 2.2 × 10^(9) N/m²

Thus;

Δp = 2.2 × 10^(9)[0.0905]

Δp = 1.991 × 10^(8) N/m²

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3 years ago
A lithium atom has three protons, three neutrons, and three electrons. What is the overall charge on this atom?
Marizza181 [45]

Answer:

0

Explanation:

The overall charge on this atom is 0.

  To find the charge on an atom;

           charge  = number of protons - number of electrons.

Note:

  • Protons are the positively charged particles in an atom
  • Electrons are the negatively charged particles in an atom
  • Neutrons carries no charges on them.

Since the atom is made up of equal number of protons and electrons, the charge on it is 0.

If the number of electrons is more, the atom will be negatively charge but if the number of protons is more, it will be positively charged.

8 0
3 years ago
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