Two resistors of resistances R1 and R2, with R2>R1, are connected to a voltage source with voltage V0. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current Ip from the source is equal to 10Is.
Let r be the ratio R1/R2R1/R2. Find r.

Answers

Answer 1

When two resistors of resistances R1 and R2, with R2>R1, are connected to a voltage source with voltage V0, the ratio r = R1/R2 is 0.127

Given the resistance of first resistor = R1

The resistance of second resistor = R2

The voltage of source = V0

The resistors are connected in series then current through it = Is.

We know that from Ohm's law V = IR where I is current.

If resistors are connected in series then Req = R1 + R2

Then V0 = Is(Req) = Is(R1+R2)

When resistors are connected in parallel current through it = Ip.

Similarly equivalent resistance of resistors connected in parallel = Req'

1/Req' = 1/R1 + 1/R2

Then 1/Req' = R1 + R2/R1R2

Req' = R1R2/R1 + R2

Therefore V0 = Ip(R1R2/R1 + R2)

From the above equations we see that as voltages remain same,

Is(R1+R2) = Ip(R1R2/R1 + R2)

Given the current Ip = 10Is. Then

Is(R1+R2) = 10Is(R1R2/R1 + R2)

(R1+R2)^2 = 10R1R2

R1^2 + R2^2 = 8R1R2

Divide LHS and RHS by R2^2 such that

8R1/R2 = (R1/R2)^2 + 1 given r = R1/R2 by substitution we get

8r = r^2+1. So, r = 0.127 (R2>R1)

Hence the required ratio of R1/R2 = 0.127

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Related Questions

assume that an mx missile goes from rest to a suborbital velocity of 6.50 km/s in 30.0 s (the actual speed and time are classified). what is its average acceleration in m/s2?

Answers

216.66 m/s² is average acceleration of mx missile.

Given information:

initial velocity, u = 0m/s

final velocity, v = 6.5km/s = 6500 m/s

time taken, t = 40s

To calculate average acceleration:

             a = [tex]\frac{( v - u)}{t}[/tex]

             a = [tex]\frac{(6500 - 0)}{30}[/tex]

             a = 216.66 m/s²

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Answers

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G

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S

Answers

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Answers

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Detailed answer of the given question.

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A projectile is launched at an angle of 15 degrees above the horizontal and lands down range. For the same speed, what other projection angle would produce the same downrange distance

Answers

For the same speed, and for the maximum downrange distance the angle would be 45°. If the projectile is launched at an angle of 15° above the horizontal.

If the initial velocity of the launched projectile = u

Horizontal component of the u, = ucosθ

Vertical component of the u, = usinθ

Horizontal downrange, R = ucosθ×T

T = usinθ/g

R = ucosθ × usinθ/g

R = u²sin(2θ)/(2g)

R = 0.25u²/g

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θ = 45°

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= u²/(2g)

= 0.5u²/g

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A particle is located at coordinates x = 2.0 m, y = 3.0 m. What is the magnitude of the torque about the origin when the particle is acted upon by a force of magnitude 5.0 N in (a) the positive x direction, (b) the positive y direction, and (c) the negative x direction?

Answers

The positive x direction is 0 Nm, positive y direction is 10 Nm, negative x direction is 0 Nm.

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In the case of (a) positive x direction, the torque about the origin is given by:

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4) a child in a tree house uses a rope attached to a basket to lift a 22 n dog into the house with a work done of 103.4 j. how far did the child lift the dog?

Answers

The distance up to where the child lift the dog into the house with a work done of 103.4 j is found to be 4.7 m.

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The work done by a force is equal to:

W = Fd

where,

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F is the force applied

The force is exerted over the distance (d).

For our case, the mass of the dog is equivalent to the force required to hoist it:

F=22 N

and the work done by the child to lift the dog is 103.4 j.

To calculate the distance is:

W = Fd

d = W / F

 = 103.4 / 22

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Therefore , the dog is moved through a distance of 4.7 m

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State the basic assumptions of the kinetic theory.

Answers

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a positive and a negative charge, each of magnitude 1.5 x 10-5 c, are separated by a distance of 15 cm. find the force on each of the particles.

Answers

15 cm separates a positive charge from a negative charge that are both 1.5 x 10-5 c in size. determine each particle's force. It exerts a force of about -89.9 N.

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A 20,000 kg rocket has a rocket motor that generates 3.0 x 10^5 N of thrust. a. What is the rocket's initial upward acceleration? b. At an altitude of 5.0 Km the rocket's acceleration has increased to 6.0 m/s^2.
What mass of fuel has it burned?

Answers

a. Rocket’s initial upward acceleration is 5.2m/s²

b. Mass of fuel has it burned is 1013 kg

Newton's second law of motion said :

∑F = m . a

The difference between the weight and the thrust will be the sum of force.

∑F = T - W

T - W = m x a

a = [tex]\frac{T - W}{a}[/tex]

From the question we know below information

m = 20000 kg = 2 x [tex]10^{4}[/tex]

T = 3.0 x [tex]10^{5}[/tex] N

W = m x g = 20000 x 9.8 = 1.96 x [tex]10^{5}[/tex] N

We just substitute the information above into the formula :

a = [tex]\frac{3.0 x 10^{5} - 1.96 x 10^{5} }{2 x 10^{4} }[/tex]

a = [tex]\frac{1.04 x 10^{5} }{2 x 10^{4} }[/tex]

a = 5.2 m / [tex]s^{2}[/tex]

So,  rocket's initial upward acceleration is 5.2m/s²

(b) The mass of the fuel that burned can be calculated as follows:

T = [tex]m_{2}a + m_{2}g[/tex]

T = [tex]m_{2} ( a + g)[/tex]

[tex]m_{2} = \frac{T}{a+g} \\[/tex]

     = [tex]\frac{3 x 10^{5} }{6 + 9.8}[/tex]

     = 18987 kg

The mass of fuel = 20000 - 18987 =  1013 kg

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A longitudinal wave has a compression to compression distance of 10 m it takes the wave of 5s to pass a point what is the wavelength of the longitudinal wave

Answers

The wavelength of the longitudinal wave will be 10meters.

What is wavelength?

The wavelength is described as the spatial period of a periodic wave which is the distance over which the wave's shape repeats.

wavelength = v/frequency

frequency = 1/T

frequency = 1/5

velocity= 10/5 = 2m/s

Therefore the  wavelength of the longitudinal wave = 2/ 0.2

 wavelength = 10meters

The wavelength is the distance between two wave crests, and it will be the same for troughs.

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what are the two best ways to measure the distance to a distant, isolated spiral galaxy, and how would it be measured

Answers

The two best ways to measure the distance to a distant, isolated spiral galaxy are by using the redshift of the galaxy and/or by using the Cepheid variable star method.

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Distance is a numerical measurement of how far apart two objects, points, or locations are. It is a measure of space in terms of length, width, or height. Distance can be measured in a variety of units including miles, kilometers, yards, and feet. Distance can also be measured in time, such as the amount of time it takes to travel from one location to another. Distance is an important concept in many areas of life, from transportation to navigation to sports.
The redshift of a galaxy is a measure of the expansion of the universe, and is determined by the Doppler Effect. It is calculated using the wavelength of a galaxy's light and the frequency of that light. Redshift can be used to measure the distance of a galaxy by comparing the redshift of the galaxy with the redshift of a standard reference. The further away a galaxy is, the greater its redshift will be.

The Cepheid variable star method is also a reliable way of measuring the distance of a distant spiral galaxy. Cepheid variable stars are stars that pulsate at a regular period, and they can be used as a “standard candle” of sorts, because their luminosity is related to their period. By measuring the period and luminosity of Cepheid variable stars in a distant spiral galaxy, astronomers can calculate the distance to that galaxy.

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A house uses solar cells that generate 1.5 kw of electrical power to supply some of its energy needs. if the solar panels supply the house with 40 percent of the power it needs, how much power does the house use?

Answers

The electric power that the house use is 3.75kW.

According to the question, a house use solar cell that gives 1.5kW of electric power and the solar panels supply the house with the 40% of the power it need.

Voltage, or the potential of a charge to produce energy, and current, or the flow of electric charge, are the two main components of electric power. Any ratio of current and voltage values can provide a given amount of power.

Let there is x kW power that the house use.

Now it is given that 40% of the power is supplied that means

40% of x=1.5

x=[tex]\frac{(1.5)(100)}{40}[/tex]

x=3.75kW

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Capacitor 2 has half the capacitance and twice the potential difference as capacitor 1.
What is the ratio Uc1/Uc2.

Where would I start with this problem and what equation would I use?

Answers

You can start the problem by using the formula for capacitance, C = Q/V, where C is the capacitance, Q is the charge stored on the capacitor, and V is the potential difference across the capacitor.

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A capacitor is a passive electrical component that stores electrical energy in an electric field. It consists of two conductive plates, separated by an insulating material called the dielectric. When a voltage is applied across the conductive plates, an electric field is created, which stores energy in the dielectric. The ability of a capacitor to store electrical energy is measured in farads (F).

Given that Capacitor 2 has half the capacitance and twice the potential difference as Capacitor 1, you can express the capacitance and potential difference of Capacitor 2 in terms of those of Capacitor 1.

C₂ = 1/2 × C₁ V₂ = 2 × V₁

You can use these equations to find the ratio of the stored energy in the two capacitors. The stored energy in a capacitor is given by the formula U = 1/2CV², where U is the stored energy, C is the capacitance, and V is the potential difference.

Uc1 = 1/2C₁V₁² Uc2 = 1/2C₂V₂²

By substituting the values of C₂ and V₂ in terms of C₁ and V₁, you can find the ratio of the stored energy in the two capacitors:

Uc1/Uc2 = (1/2C₁V₁²) / (1/2×(1/2C₁) (2V₁) ²) Uc1/Uc2 = 1/8

The ratio of stored energy in the two capacitors is 1/8.

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you decide to use your garden hose to wash your garage door. the water shoots out at a rate of 10 kg/s and a speed of 16 m/s with respect to the hose. when the water hits the garage, its speed decreases to zero. determine the force that the water exerts on the wall. what assumptions did you make?

Answers

The force exerted by the water on the wall will be equal to 160 N. Newton's third law of motion is seen taking place here.

How is force exerted by the water on the wall calculated?

The force exerted by the water on the wall is calculated using the impulse-momentum principle. The principle states that the change in momentum of an object is equal to the impulse, or the force applied over a certain period of time. In this case, the change in momentum is equal to the initial momentum of the water (mass flow rate multiplied by velocity) minus the final momentum of the water (mass flow rate multiplied by final velocity) and the time is assumed to be very small.

What assumptions were made in the calculation of force exerted by the water on the wall?

The assumptions made in the calculation of force exerted by the water on the wall are:

The water hits the garage instantaneously.

The water flow rate is constant and no water is lost during the impact.

The water hits the garage uniformly over the entire area and not just at one point.

The garage door is not moving before the impact. These assumptions are made to simplify the calculation and to make it more accurate. It is important to note that in real-world scenarios, these assumptions may not always hold true and the force exerted by the water on the wall may be different.

How do you calculate the force exerted by water on the wall?

Force exerted by the wall on the water, F = dP/dt

= (P2 - P1)/dt

= dm*(V2 - V1)/dt

= (V2 - V1) x dm/dt

= (0 - 16) x 10

= -160 N (negative sign indicates force opposes the motion)

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a certain 48 v electric forklift can lift up to 7000 kg at a maximum rate of 75 meters per minute. what is its power? round your answer to the nearest hundreds.

Answers

In this case  the power is 703.8 kW and rounding to the nearest hundreds gives 700 kW.

What is power?

Power is the ability to influence or control people, events, and outcomes. It can be seen when one person or group is able to make decisions, set standards, and enforce boundaries. Generally, power is associated with authority, control, and influence; however, it can also refer to the capacity to do work or generate energy.

The power of the forklift can be calculated using the formula: Power = (Load x Velocity) / Time.

In this case, the power is (7000 kg x 75 m/min) / 1 min = 525,000 kg•m/min. Converting to watts, this is 525,000 kg•m/min / 746 = 703.8 kW.

Rounding to the nearest hundreds gives 700 kW.

In this case  the power is 703.8 kW and rounding to the nearest hundreds gives 700 kW.

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when you used a stiffer or tighter elastic material, what effect did this have on the duration of the impulse? what effect did this have on the maximum size of the force? can you develop a general rule from these observations?

Answers

The use of a stiffer or tighter elastic material caused the duration of the impulse to be shorter, making the maximum force larger.

The general rule that can be formed would be that the shorter the time, the larger the force is to achieve the same impulse.

We can define it by impulse- momentum theorem.

Ft = mΔv( also, Ft = impulse)

F = mΔv/ t

Impulse is commensurable to the constant net force acting on an object and the time period that the net force acts.

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