1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lozanna [386]
2 years ago
14

Find the value of currents through each branch

Physics
1 answer:
Irina-Kira [14]2 years ago
8 0

Answer:

the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

Explanation:

You can write the KVL equations:

Top left loop:

  I2(4) +(I2 +I3)(2) +I1(1) = 10

Bottom left loop:

  (I1-I2)(4) +(I1-I2-I3)(2) +I1(1) = 10

Right loop:

  (I2+I3)(2) +(I2+I3-I1)(2) = 5

In matrix form, the equations are ...

  \left[\begin{array}{ccc}1&6&2\\7&-6&-2\\-2&4&4\end{array}\right]\cdot\left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}10\\10\\5\end{array}\right]

These equations have the solution ...

  \left[\begin{array}{c}I_1\\I_2\\I_3\end{array}\right] =\left[\begin{array}{c}2.500\\0.625\\1.875\end{array}\right]

This means the branch currents are as follows:

  top left: I2 = 0.625 A

  middle left: I1 = 2.500 A

  bottom left: I1-I2 = 1.875 A

  top center: I2+I3 = 2.500 A

  bottom center: I2+I3-I1 = 0 A

  right: I3 = 1.875 A

_____

This can be worked almost in your head by using the superposition theorem. When the 5V source is shorted, the 10V source is supplying (I1) to a circuit that is the 4 Ω and 2 Ω resistors in parallel with their counterparts, and that 2+1 Ω combination in series with 1 Ω for a total of a 4Ω load on the 10 V source. That is, I1 due to the 10V source is 2.5 A, and it is nominally split in half through the upper and lower branches of the circuit. There is no current flowing through the (shorted) 5 V source branch.

When the 10V source is shorted, the 5V source is supplying a 4 +4 Ω branch in parallel with a 2 +2 Ω branch, a total load of 8/3 Ω. This makes the current from that source (I3) be 5/(8/3) = 15/8 = 1.875 A. There is zero current from this source through the 1 Ω resistor.

Nominally, the current from the 5V source splits 2/3 through the 2 Ω branch and 1/3 through the 4 Ω branch.

Using superposition, I2 = I1/2 -I3/3 = (2.5 A/2) -(1/3)(15/8 A) = 0.625 A. This is the same answer as above, without any matrix math.

  (I1, I2, I3) = (2.5 A, 0.625 A, 1.875 A)

__

It helps to be familiar with the formulas for resistors in series and parallel.

You might be interested in
How a diode can act as a capacitor?
maks197457 [2]

A diod can act as a capacitor the deplition region in diod acts as a capacitor as it also stores energy similar to capacitor in electric field.

3 0
2 years ago
What is the mass of a dog running at a speed of 5 m/s and a momentum of 120.5 kgm/s?
viktelen [127]

Given:

Momentum of the dog (p) = 120.5 kg m/s

Speed of the dog (v) = 5 m/s

To Find:

Mass of the dog (m)

Concept/Theory:

\underline{\underline{ \bf{\Large{Momentum}}}}

  • It is defined as the quantity of motion contained in a body.
  • It is measured as the product of mass of the body and it's speed.
  • It is represented by p.
  • It's SI unit is kg m/s
  • Mathematical Representation/Equation of Momentum: \boxed{ \bf{p = mv}}

Answer:

By using equation of momentum, we get:

\rm \longrightarrow m =  \dfrac{p}{v}  \\  \\  \rm \longrightarrow m =  \dfrac{120.5}{5}  \\  \\  \rm \longrightarrow m = 24.1 \: kg

\therefore Mass of the dog (m) = 24.1 kg

6 0
2 years ago
What units must the constant G have in order for the u it’s F to be newtons (N)?
EleoNora [17]

The units for G must be [N][m^2][kg^{-2}]

Explanation:

The magnitude of the gravitational force between two objects is given by:

F=G\frac{m_1 m_2}{r^2}

where

F is the force

G is the gravitational constant

m_1, m_2 are the masses of the two objects

r is the separation between the objects

We know that:

  • The units of F are Newtons (N)
  • The units of m_1,m_2 are kilograms (kg)
  • The units of r are metres (m)

So, we can rewrite the equation in terms of G, to find its units:

G=\frac{Fr^2}{m_1 m_2}=\frac{[N][m]^2}{[kg][kg]}=[N][m^2][kg^{-2}]

Learn more about gravitational force:

brainly.com/question/1724648

brainly.com/question/12785992

#LearnwithBrainly

5 0
2 years ago
An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its angular frequency is: 0. 79 rad/s 1. 57 rad/s 2
morpeh [17]

Angular frequency in radian per second for 20 vibrations in 10 seconds is 12.6 rad/s

<h3>What is Angular frequency?</h3>

Angular frequency is the number of vibrations in radian per second.

The total number of vibrations n is 20 and the time taken for these vibrations is 10 s

The frequency of the vibrations will be

f = 20 / 10 = 2 Hz

Angular frequency is related to the frequency as

ω = 2πf

ω=2π × 2

ω = 12.6 rad/s

Thus, the angular frequency is 12.6 rad/s.

Learn more about Angular frequency.

brainly.com/question/14244057

#SPJ

5 0
2 years ago
Light from a 560 nm monochromatic source is incident upon the surface of fused quartz (n=1. 56) at an angle of 60°. what is the
ankoles [38]

The angle of reflection is "60°".

Here we apply the law of the concept of reflection then we get the final answer easily.

The angle of incident = angle of reflection

Then, the Angle of the incident =60°

What is reflection?

  • Reflection is the phenomenon of light rays returning to the source after striking an obstruction.
  • It resembles the way a ball bounces when we toss it on a hard surface.
  • Some of the light rays that strike an item are reflected, some of them travel through it, and the remainder are absorbed by the object.
  • The given values are:Light from a monochromatic source,= 560 nm
  • The angle of incidence,= 60°
  • The surface of fused quartz (n),= 1.56
  • When a light ray does exist on a flat surface, the law or idea of reflection should apply since it includes both the reflected and "normal" light rays at the mirror surface.
  • According to the above law,Angle of incident = angle of reflection
  • Then, Angle of incident =60°.

To learn more about reflection visit: brainly.com/question/15487308

#SPJ4

7 0
1 year ago
Other questions:
  • PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
    10·1 answer
  • Two hoops, starting from rest, roll down identical inclined planes. The work done by nonconservative forces, such as air resiste
    12·1 answer
  • A perfectly conductive plate is placed in the y z-plane. An electromagnetic wave with electric field is incident on the conducto
    8·1 answer
  • Monitoring your grades will help you pinpoint your academic weaknesses. true or false.
    6·2 answers
  • A standing wave of the third harmonic is induced in a stopped pipe of length 1.2 m. The speed of sound through the air of the pi
    13·1 answer
  • Ball 1 is thrown to the ground with an initial downward speed; ball 2 is dropped to the ground from rest.
    9·1 answer
  • A moving object has a kinetic energy of 150J and a momentum of 20.3kgxm/s find the speed of the object in m/s
    15·1 answer
  • Chuyển động thẳng đều là gì
    7·1 answer
  • SOMEONE, PLEASE HELP ME AS FAST AS YOU CAN, I WOULD GIVE MORE POINTS BUT THIS IS THE REST OF MY POINT, PLEASE SOMEONE WHO IS SUP
    5·1 answer
  • When capacitors are connected in parallel, they have the same:.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!