An air conditioner uses 10,832 J of energy to run, but only 5,488 J of energy is used to heat or cool the air of a home. What is its energy efficiency?

The total charge in the circuit is 240 microcoulombs.

To calculate the total charge in a series circuit with capacitors, we need to use the formula Q = CV, where Q represents the charge, C is the capacitance, and V is the voltage.

In this case, we have three capacitors connected in series with capacitances of 4 μF, 3 μF, and 2 μF, respectively. The voltage across the circuit is 260 V.

To find the total capacitance (C_total) in a series circuit, we use the reciprocal rule: 1/C_total = 1/C1 + 1/C2 + 1/C3. Plugging in the values, we get 1/C_total = 1/4 + 1/3 + 1/2.

Simplifying this equation gives us 1/C_total = (3 + 4 + 6)/12 = 13/12. Taking the reciprocal, we find C_total = 12/13 μF.

Now, we can calculate the total charge (Q_total) using Q = C_total × V. Substituting the values, we get Q_total = (12/13) μF × 260 V.

Calculating the numerical value, Q_total = (12/13) × 260 = 240 μC (microcoulombs).
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According to Newton's second law of motion, 12.8 N is the average force of the Puck

It states that, the rate of change of momentum is directly to the force applied. That is,

F = m(v - u)/t

Given that a 0.16 k/g hockey puck is moving on an icy Horizontal service with the speed of 5 m/s player strikes the Puck by hockey stick after the impact the Puck moves in opposite direction with the speed of 9 m/s of the Puck was the in contact with the stick for 0 points 0.05 s

The average force of the Puck by the stick can be calculated by using the formula above.

Where

Substitute all the parameters

F = 0.16(9 - 5)/0.05

F = 0.16(4)/0.05

F = 0.64/0.05

F = 12.8 N

Therefore, the average force of the Puck by the stick is 12.8 N

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The two different types of equilibrium discussed in the video are

1. Static equilibrium and dynamic equilibrium

Static equilibrium refers to a state where an object is at rest and the net force acting on it is zero. In other words, the forces acting on the object are balanced, so there is no acceleration. For example, a book lying on a table is in static equilibrium, as the gravitational force pulling it down is balanced by the force of the table pushing it up.

On the other hand, dynamic equilibrium refers to a state where an object is moving with a constant velocity, which means that its acceleration is zero. In this case, the net force acting on the object is also zero, but unlike static equilibrium, the object is in motion. For example, a car driving at a constant speed on a straight road is in dynamic equilibrium.

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The way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.

Option A.

An atom can be defined as the smallest part of a substance that cannot be broken down chemically. Each atom has a nucleus (center) made up of protons (positive particles) and neutrons (particles with no charge).

The arrangement of electrons in orbitals and shells around the nucleus is referred to as the electronic configuration of the atom.

Thus, we can conclude that the way in which one atom interacts with another atom is mostly influenced by the configuration of the electrons farthest from the nucleus.

The remaining options do not fit the empty space properly, and they include;

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Answer:

Average acceleration is 2.5 m/s^2.

Explanation:

Average acceleration can be found by dividing the change in speed by the change in time.

We know that the initial velocity=10m/s, the final velocity=30m/s and time elapsed is t=8s.

a= (Final velocity-Initial Velocty)/t

a=(30-10)/8=20/8=2.5 m/s^2

A proton (charge 1.602 * 10-19) moves a distance of d= 0.59 m from point A to point B in a straight line inside a linear accelerator. The electric field of the accelerator is uniform and has a magnitude of 15 MN/C.

i.) The expression for the force on proton is,

F=qE

(1.6⋅10−19 )(1.5⋅10 7)

=2.4⋅10 −12 N

Thus, the force on the proton is 2.4⋅10 −12 N.

ii) The expression for the work done by the field is,

W=qEd

(1.6⋅10 −19)(1.5⋅10 7 )(0.5)

=1.2⋅10 −12J

iii) The expression for the potential difference is,

U=Ed

=(1.5⋅10 7) (0.5)

=0.75⋅10 7 V

Electric potential of a system of point charges?

A point charge's electric potential is V=kQ/r. Electric field is a vector while electric potential is a scalar.

What is the electric potential at a point distance?

Electric potential at point P, located at a distance of r=R2 from the center, where R is the radius of an evenly charged shell with a density of surface charges.

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When Sally puts on wool socks and rubs her feet on a nylon carpet, static electricity builds up through a process involving the movement of electrons. The friction between the wool socks and the nylon carpet causes electrons from the wool socks to move to the carpet, resulting in Sally and her socks gaining a negative charge.

The correct answer would be the friction causes electrons from the wool socks to move to Sally, giving Sally a negative charge.

The friction between the wool socks and the nylon carpet causes electrons from the wool socks to move to the carpet, resulting in Sally and her socks gaining a negative charge. This is due to the phenomenon known as the triboelectric effect.

The triboelectric effect occurs when two materials come into contact and then separate. During the rubbing process, the atoms in the two materials interact, causing the transfer of electrons between them. In this case, the wool socks have a greater affinity for electrons compared to the nylon carpet. As a result, electrons from the socks are transferred to the carpet, leaving the socks with a positive charge and the carpet with a negative charge.

Sally, wearing the wool socks, experiences an accumulation of excess electrons on her feet, giving her a negative charge. This excess negative charge on her body can lead to static electricity-related phenomena, such as experiencing a shock when touching a metal object or seeing her hair stand on end when near certain surfaces.

It's important to note that the movement of electrons determines the charge distribution during the triboelectric effect. In this scenario, electrons move from the wool socks to the nylon carpet, resulting in Sally and her socks gaining a negative charge.

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Answer:

F' = 162 units

Explanation:

The gravitational force of attraction between the two objects is given by Newton's Gravitational law through the following formula:

\(F = \frac{Gm_{1}m_{2}}{r^{2}}\\\\\)

where,

F = gravitational force = 18 units

G = Gravitational Constant

m₁ = mass of object 1

m₂ = mass of object 2

r = distance between objects

Therefore,

\(18 = \frac{Gm_{1}m_{2}}{r^{2}}------ eqn (1)\\\\\)

Now, if we change the value of distance to one-third of original value, then:

r' = r/3

\(F' = \frac{Gm_{1}m_{2}}{(\frac{r}{3})^{2}}\\\\F' = (9)(\frac{Gm_{1}m_{2}}{r^{2}})\)

using eqn (1):

F' = 9(18 units)

F' = 162 units

The coefficient of  static friction between the tires and the road is 1.987.

Radius of the track, r =  516 m, Tangential Acceleration =  3.89 m/s^2 and Speed,v =  32.8 m/s

The radial Acceleration is given by, Now the total acceleration is The frictional force on the car will be f = ma------------(1)

And the force due to gravity is W = mg--------------------(2)

Now the coefficient of  static friction is, From (1) and (2), Substituting the values, we get friction is 1.987.

Therefore, The coefficient of  static friction between the tires and the road is 1.987.

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Atom A has 10 protons, 12 neutrons, and 10 electrons, while Atom B has 10 protons, 10 neutrons, and 12 electrons.

Atom A and Atom B are not isotopes of each other. Isotopes are atoms of the same element that differ in the number of neutrons but have the same number of protons. In this case, Atom A and Atom B have different numbers of protons, which means they are not isotopes of each other.

The number of protons determines the element, and since Atom A and Atom B have different numbers of protons, they belong to different elements.

Isotopes, on the other hand, have the same number of protons but differ in the number of neutrons.

This variation in the number of neutrons gives isotopes different atomic masses while retaining the same chemical properties.

However, Atom A and Atom B do not fulfill this criterion, so they cannot be considered isotopes of each other.

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The equation that shows work being calculated using the correct units is as follows: 113J = (17.4 N) x (6.51 m) {option B}.

Work done is a measure of energy expended in moving an object. It is most commonly calculated by multiplying force by distance. No work is done if the object does not move.

Work done is measured in Joules, which is equivalent to Newtons/metres (N/m).

Joules is the derived unit of energy, work and heat; the work required to exert a force of one newton for a distance of one metre.

Newton is the unit of measurement for force while metres is the unit of measurement for distance, hence, to calculate a work done of 113 Joules, 17.4 Newtons of force over a distance of 6.51 metres is needed.

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Answer:

It's 113 j = (17.4N) x (6.51)

Explanation:

Your welcome

Complete Question

The complete question is shown on the first uploaded image

Answer:

Explanation:

From the question we are told

   The amplitude of the lateral  force is  \(F = 25 \ N\)

   The frequency is   \(f = 1 \ Hz\)

   The mass of the bridge per unit length is  \(\mu = 2000 \ kg /m\)

    The length of the central span is  \(d = 144 m\)

     The oscillation amplitude of the section  considered at the time considered is  \(A = 75 \ mm = 0.075 \ m\)

      The time taken for the undriven oscillation to decay to \(\frac{1}{e}\)  of its original value is  t = 6T

Generally the mass of the section considered is mathematically represented as

            \(m = \mu * d\)

=>        \(m = 2000 * 144\)

=>        \(m = 288000 \ kg\)

Generally the oscillation amplitude of the section after a  time period  t is mathematically represented as

                 \(A(t) = A_o e^{-\frac{bt}{2m} }\)

Here b is the damping constant and the \(A_o\) is the amplitude of the section when it was undriven

So from the question  

               \(\frac{A_o}{e} = A_o e^{-\frac{b6T}{2m} }\)

=>            \(\frac{1}{e} =e^{-\frac{b6T}{2m} }\)

=>          \(e^{-1} =e^{-\frac{b6T}{2m} }\)

=>           \(-\frac{3T b}{m} = -1\)

=>         \(b = \frac{m}{3T}\)

Generally the amplitude of the section considered is mathematically represented as

           \(A = \frac{n * F }{ b * 2 \pi }\)

=>       \(A = \frac{n * F }{ \frac{m}{3T} * 2 \pi }\)

=>       \(n = A * \frac{m}{3} * \frac{2\pi}{25}\)

=>       \(n = 0.075 * \frac{288000}{3} * \frac{2* 3.142 }{25}\)

=>       \(n = 1810 \ people\)

A bicycle slows down uniformly from vi=8.40 [m/s] to rest over a distance of 115 [m]. Each wheel and tire has an overall diameter of 0.68 [m]. The magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².

To determine the magnitude of the angular acceleration of the wheel, we need to first calculate the change in angular velocity and the time taken to come to rest. Then we can use these values to find the angular acceleration.

Calculate the initial angular velocity:

The initial linear velocity of the bicycle wheel is given by the formula v = ω * r, where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.

The radius of the wheel is half the diameter, so r = 0.68 m / 2 = 0.34 m.

Given the initial linear velocity vi = 8.40 m/s, we can calculate the initial angular velocity ωi:

vi = ωi * r

ωi = vi / r

Calculate the final angular velocity:

The final angular velocity of the wheel is 0 rad/s since it comes to rest.

ωf = 0 rad/s

Calculate the change in angular velocity:

The change in angular velocity (Δω) is given by the formula Δω = ωf - ωi.

Δω = 0 - ωi

Calculate the time taken to come to rest:

To calculate the time taken to come to rest, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Given the initial velocity vi = 8.40 m/s, final velocity vf = 0 m/s, and distance d = 115 m, we can calculate the acceleration a:

vf = vi + at

0 = 8.40 + a * t

We also know that the distance traveled d is related to the initial and final velocities and the time by the formula d = (vi + vf) / 2 * t:

d = (vi + vf) / 2 * t

115 = (8.40 + 0) / 2 * t

From the two equations above, we can solve for the acceleration a and the time t.

Calculate the angular acceleration:

The angular acceleration (α) is given by the formula α = Δω / t.

α = Δω / t

Substitute the values for Δω and t and calculate the angular acceleration.

Therefore, the magnitude of the angular acceleration of the wheel is approximately 0.0757 rad/s².

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Answer:

C , E , A , D , B

Explanation:

We evaluate the accelerations for each case, using the formula: a = (vf - vi) / t

A)  a = (10.3 - 0.5 ) / 1 = 9.8 m/s^2  --> magnitude: 9.8 m/s^2

B)  a = (0 - 20) / 1 = - 20 m/s^2  -->  magnitude : 20 m/s^2

C)  a = (0.02 - 0.004) / 1 = 0.016 m/s^2 -->  magnitude : 0.016  m/s^2

D)  a = (4.3 - 0) / 0.4 = 10.75 m/s^2  -->  magnitude : 10.75 m/s^2

E)  a = (1 - 2) / 8.3 = - 0.12 m/s^2  -->  magnitude: 0.12 m/s^2

Then, comparing magnitudes from least to greatest:

C , E , A , D , B

The order of the magnitude of the acceleration, from least to greatest is:

C < E < A < D < B

In physics, acceleration (a) is the rate at which velocity changes (Δv) with time (t).

We will calculate the acceleration for each scenario using the following expression.

\(a = \frac{v-u}{t}\)

where,

Data

\(a = \frac{10.3m/s-0.50m/s}{1.0s} = 9.8 m/s^{2}\)

Data

\(a = \frac{0m/s-20m/s}{1.0s} = -20 m/s^{2}\\\\|a| = 20 m/s^{2}\)

Data

\(a = \frac{2.0cm/s-0.40cm/s}{0.50s} = 3.2cm/s^{2} \times \frac{1m}{100cm} = 0.032 m/s^{2}\)

Data

\(a = \frac{4.3m/s-0m/s}{0.40s} = 11 m/s^{2}\)

Data

\(a = \frac{1.0m/s-2.0m/s}{8.3s} = -0.12 m/s^{2}\\\\|a| = 0.12 m/s^{2}\)

The order of the magnitude of the acceleration, from least to greatest is:

C < E < A < D < B

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Answer:

Explanation:

Charge on uranium ion = charge of a single electron

= 1.6 x 10⁻¹⁹ C

charge on doubly ionised iron atom = charge of 2 electron

= 2 x 1.6 x 10⁻¹⁹ C = 3.2 x 10⁻¹⁹ C

Let the required distance from uranium ion be d .

force on electron at distance d from uranium ion

= 9 x 10⁹ x 1.6 x 10⁻¹⁹ / r²

force on electron at distance 61.10 x 10⁻⁹ - r from iron  ion

= 9 x 10⁹ x 3.2 x 10⁻¹⁹ / (61.10 x 10⁻⁹ - r )²

For equilibrium ,

9 x 10⁹ x 1.6 x 10⁻¹⁹ / r² = 9 x 10⁹ x 3.2 x 10⁻¹⁹ / (61.10 x 10⁻⁹ - r )²

2 d² = (61.10 x 10⁻⁹ - r )²

1.414 r = 61.10 x 10⁻⁹ - r

2.414 r = 61.10 x 10⁻⁹

r = 25.31 nm .

(a)  The distance from the uranium atom at which an electron will be in equilibrium is \(2.04 \times 10^{-8} \ m\)

(b) The magnitude of the force on the electron from the uranium ion is \(3.46 \times 10^ 6 \ N\)

The given parameters:

The force on the electron due to uranium ion at distance r is calculated as follows;

\(F _1 = \frac{Kq_1^2}{r^2} \\\\F_1 = \frac{9\times 10^9 \times (1.6\times 10^{-19})^2}{r^2} \\\\F_1 = \frac{2.3 \times 10^{-28}}{r^2}\)

The force on the electron due to uranium ion at distance less than 61.10 nm.

R = 61.10 nm - r

\(F_2 = \frac{9\times 10^9 \times (3.2 \times 10^{-19})^2}{(61.1 \times 10^{-9} \ - \ r)^2} \\\\\F_2 = \frac{9.216 \times 10^{-28}}{(61.1 \times 10^{-9} \ - \ r)^2}\)

At equilibrium, the force between the electron and ions will be equal.

\(\frac{9.216 \times 10^{-28}}{(61.1 \times 10^{-9} \ - \ r)^2}= \frac{2.3 \times 10^{-28}}{r^2}\\\\\frac{4}{(61.1 \times 10^{-9} \ - \ r)^2} = \frac{1}{r^2} \\\\4r^2 = (61.1 \times 10^{-9} \ - \ r)^2\\\\2^2r^2 = (61.1 \times 10^{-9} \ - \ r)^2\\\\2r = 61.1 \times 10^{-9} \ - \ r\\\\3r = 61.1 \times 10^{-9} \\\\r = \frac{61.1 \times 10^{-9}}{3} \\\\r = 2.04 \times 10^{-8} \ m\)

The magnitude of the force on the electron from the uranium ion is calculated as follows;

\(F = \frac{kq_1^2}{r^2} \\\\F = \frac{9\times 10^9 \times 1.6\times 10^{-19}}{(2.04 \times 10^{-8})^2} \\\\F= 3.46 \times 10^6 \ N\)

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The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.

The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.

The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.

The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.

The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).

The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).

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One stands at the base of a 3.90-m long frictionless ramp that is inclined at an angle of 8.60∘, so one must give the object an initial velocity of 2.29 m/s up the ramp to slide a 1.95-kg object up the ramp.

The potential energy of the object at the top of the ramp = the initial kinetic energy of the object, as the final velocity is zero.

m × g ×h = 1/2 × m × \(v_0^2\)

(m= mass of the object, g = acceleration due to gravity, h = height of the ramp, and \(v_0\) = initial velocity of the object)

\(v_0\) =√2× g ×h

\(v_0\) =√2×  9.81 m/\(s^2\) ×3.90 m× sin(8.60°)

\(v_0\) =2.29 m/s

Hence, one stands at the base of a 3.90-m long frictionless ramp that is inclined at an angle of 8.60∘, so one must give the object an initial velocity of 2.29 m/s up the ramp.

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The question is incomplete, the complete question is below

You stand at the base of a 3.90-m long frictionless ramp that is inclined at an angle of 8.60∘. You want to slide a 1.95-kg object up the ramp so that it stops just as it reaches the top. What initial velocity must you give the object?

The pressure of the gas in the deodorant can when it is heated to 900 K is 9 atm.

Gay-Lussac's law states that the pressure exerted by a given quantity of gas varies directly with the absolute temperature of the gas.

It is expressed as;

P₁/T₁ = P₂/T₂

From the data:

We substitute our values into the expression above and solve for final pressure.

P₁/T₁ = P₂/T₂

P₁T₂ = P₂T₁

P₂ = P₁T₂  / T₁

P₂ = ( 3 atm × 900 K ) / 300 K

P₂ = 9.0 atm

Therefore, the final pressure is 9.0 atm.

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Organelles are specialized structures within cells that perform specific functions, such as energy production, protein synthesis, and waste removal.

Some examples of organelles include mitochondria, which produce energy for the cell, and ribosomes, which are involved in protein synthesis.

The size of cells can vary widely depending on the organism and the type of cell. For example, human cells can range from 10 to 30 micrometers in diameter, while bacterial cells are typically much smaller, ranging from 1 to 5 micrometers in diameter.

In summary, organelles are specialized structures within cells that perform specific functions, and the size of cells can vary widely depending on the organism and the type of cell.

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Answer: Convention

Explanation: Convention is pretty well known for being a process that transmits heat from one place to another place with the movements of heated particles. I got this answer from my notebook during my chemistry class.

Hope this answer helps!

Answer:

I would need to see the part a to be more specific but this may help:

resources like solar, water, wind are considered renewable because they will never run out, they can be replenished over and over again. There will always be a sun (and if there wasn't then we'd have bigger conserns than renewable energy) and the wind will always blow. It can never run out because you use too much unlike coal and fossil fuels.

Hope this helps!

Answer: The amount of potential energy stored in 300g object is 1,75m.

The amount of potential energy stored in the object is 13.755 J.

To determine the potential energy stored in the object, we need to know about the gravitational potential energy and how is it calculated.

      where, m=mass

                  g= gravitational field or acceleration due to gravity

                  h= height

Potential energy = 0.3×26.2×1.75=13.755J.

Thus, we can conclude that the amount of potential energy stored in a 300g object 1.75 m above Jupiter's surface would be 13.755J.

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Answer:

9 electrons

Explanation:

The structure has 9 protons and hence the number of electrons equals the number of protons that's why it is said to be electrical neutral

The average speed of the whole journey is 54 mph.

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The cost to use all lamps is $62.

           power=energy/time

          (60+ 100+150)=energy/2.5

          energy=775 joule

cost for 1 hour=$0.08

                      = 775 * 0.08

                     = $62

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Answer:

6.2 cents

Explanation:

(60+100+150/1000)*2.5*8=6.2 cents

The pressure after the temperature has risen to 40.0 °C, assuming that there are no appreciable leaks or changes in volume is 4.35×10⁵ Pa

From the question given above, the following data were obtained:

The pressure the temperature has risen to 40 °C can be obtained as follow:

P₁V₁ / T₁ = P₂V₂ / T₂

Volume = contant

P₁ / T₁ = P₂ / T₂

4.00×10⁵ / 288 = P₂ / 313

Cross multiply

P₂ × 288 = 4.00×10⁵ × 313

Divide both sides by 288

P₂ = (4.00×10⁵ × 313) / 288

P₂ = 4.35×10⁵ Pa

Thus, the pressure at 40 °C is 4.35×10⁵ Pa

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\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of Logic.

Since in the above statement it is given that,

All S are P ==> True,

then obviously Some S are also P always, hence it is true.

Answer is True.

Considering the Ohm's law, the correct answer is option d): the minimum resistance is 8 ohms.

Current is the physical quantity that expresses the amount of electricity that flows through a conductor in a unit of time. It is measured in amps.

The voltage is the difference that exists between the electrical charge that leaves the source and with which it finally reaches the end of the circuit. It is expressed in volts.

Finally, resistance is the difficulty that a circuit opposes to the passage of a current. They are measured in ohms.

Ohm's Law relates the magnitudes of voltage, resistance, and intensity. Ohm's law says that "the intensity of the electric current flowing through an electric conductor is directly proportional to the applied potential difference and inversely proportional to its resistance".

Mathematically Ohm's law is expressed as:

\(I=\frac{V}{R}\)

Then, knowing the intensity and the voltage, it is possible to calculate the resistance as follows:

\(R=\frac{V}{I}\)

In this case, you know:

Replacing in Ohm's Law:

\(R=\frac{120 V}{15 A}\)

Solving:

R= 8 ohms

Finally, the correct answer is option d): the minimum resistance is 8 ohms.

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Answer:

See explanation

Explanation:

a) Formula for the mass of the sample that remains after t years = N= Noe^-kt

Where;

N = mass at time t years

No = mass at time t= 0

k = decay constant

t = time taken

So,

N = 100e^-kt

b) First,

t1/2 = -ln(1/2)/k

t1/2 = 0.693/k

t1/2 = half life of radium-226 =1590 years

1590 = 0.693/k

k = 0.693/1590

k = 4.36 * 10^-4

So,

N= 100e^-(4.36 * 10^-4 * 1000)

N= 65 mg

c) From

N = 100e^-kt

40 = 100e^-(4.36 * 10^-4t)

40/100 = e^-(4.36 * 10^-4t)

0.4 = e^-(4.36 * 10^-4t)

ln(0.4) = ln(e^-(4.36 * 10^-4t))

-0.9163 = -4.36 * 10^-4t

t = 0.9163/4.36 * 10^-4

t = 2102 years