Let's find the angle theta between the vectors u and v. Recall that the dot product between two vectors is defined as the product of their magnitudes and the cosine of the angle between them.
That isu · v = |u| |v| cos(theta)Rearranging this formula, we obtain
cos(theta) = (u · v) / (|u| |v|)
Note that
|u| = [tex]sqrt(4^2 + 3^2)[/tex]
= 5 and
|v| =[tex]sqrt(5^2 + (-12)^2)[/tex]
= 13.
Therefore,
u · v = 4*5 + 3*(-12)
= -8
Thus,cos(theta) = -8 / (5 * 13)
= -8/65.
Now, let's find the angle theta using a calculator. The inverse cosine function (denoted cos^(-1)) of -8/65 is given bytheta = [tex]cos^(-1)(-8/65)[/tex]We can convert this angle to degrees or radians as required by the problem. If we use degrees, then we have to convert the angle from degrees to radians using the formula radians = (pi / 180) * degrees. If we use radians, then we simply leave the answer in radians.Let's use radians, and round to two decimal places. Thus,
theta = [tex]cos^(-1)(-8/65)[/tex]
≈ 1.84
Therefore, the angle between the vectors u and v is approximately 1.84 radians.
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A person inhales and exhales 1.5 L of 38 °C air, evaporating of 0.04 g water from the lungs and breathing passages with each breath. The latent heat of vaporization of water is 2430 × 10³ J/kg. Use 1 L = 10-³m³. Density of air = 1.29 kg/m³, and the specific heat of air is 721 J/(kg°℃) (a) How much heat transfer occurs due to evaporation in each breath? Heat transfered in each breath = (b) What is the rate of heat transfer in watts if the person is breathing at a moderate rate of 18.0 breaths per minute? Rate of heat transfer= W (c) If the inhaled air had a temperature of 20 °C, what is the rate of heat transfer for warming the air? Think & Prepare 1. To raise the temperature of air from 20°C to 38°C, how much heat is required? 2. How will you calculate the mass of air from its volume and density? 3. Use the breathing rate to calcuate the rate of heat transfer in W. Rate of heat transfer= W (d) Discuss the total rate of heat transfer as it relates to typical metabolic rates. Will this breathing be a major form of heat transfer for this person? Total heat tranfer during to two processes W
In each breath, 0.04 g of water evaporates, resulting in a heat transfer of 97.2 J due to evaporation. At a breathing rate of 18 breaths per minute, the rate of heat transfer is 29.13 W. Additionally, warming the inhaled air from 20°C to 38°C contributes a heat transfer of 22.128 J. The total rate of heat transfer per breath is 119.328 J. However, compared to overall metabolic heat production, breathing is a minor form of heat transfer for this person.
(a) To calculate the heat transferred due to evaporation in each breath, we need to find the amount of heat required to evaporate the water.
The formula for heat transfer due to evaporation is Q = m × Lv, where Q is the heat transfer, m is the mass of water evaporated, and Lv is the latent heat of vaporization of water.
Here, m = 0.04 g and Lv = 2430 × 10³ J/kg. Converting the mass to kilograms, we get m = 0.04 × 10⁻³ kg. Substituting the values, we find Q = (0.04 × 10⁻³ kg) × (2430 × 10³ J/kg) = 97.2 J.
(b) The rate of heat transfer in watts can be calculated by dividing the total heat transfer by the time taken.
Given that the breathing rate is 18.0 breaths per minute, the time for each breath is 1 minute / 18 breaths = 1/18 minutes = (1/18) × 60 seconds.
Thus, the rate of heat transfer is 97.2 J / [(1/18) × 60 s] = 97.2 J / 3.33 s = 29.13 W.
(c) To calculate the rate of heat transfer for warming the air, we need to determine the amount of heat required to raise the temperature of air from 20°C to 38°C.
The formula for heat transfer due to temperature change is Q = m × c × ΔT, where m is the mass of air, c is the specific heat of air, and ΔT is the change in temperature.
We can calculate the mass of air using the density of air and the volume of air inhaled and exhaled in each breath. The volume of air is given as 1.5 L, which is equal to 1.5 × 10⁻³ m³.
The density of air is 1.29 kg/m³. Thus, the mass of air is (1.5 × 10⁻³ m³) × (1.29 kg/m³) = 1.935 × 10⁻³ kg. Substituting the values, we find Q = (1.935 × 10⁻³ kg) × (721 J/(kg°℃)) × (38°C - 20°C) = 22.128 J.
(d) The total rate of heat transfer for each breath is the sum of the heat transfer due to evaporation and the heat transfer for warming the air.
Thus, the total rate of heat transfer per breath is 97.2 J + 22.128 J = 119.328 J.
Considering the breathing rate of 18 breaths per minute, the total rate of heat transfer would be 119.328 J/breath × 18 breaths/minute = 2147.904 J/minute.
This form of heat transfer through evaporation and warming of inhaled air is relatively small compared to the overall metabolic heat production in the human body.
Metabolic rates are typically in the range of hundreds to thousands of watts, while the heat transfer rate in this case is only 2147.904 J/minute, equivalent to approximately 35.798 W.
Therefore, breathing alone is not a major form of heat transfer for this person compared to other metabolic processes.
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Over the Gurney Flap configuration, the horizontal freestream flow with a velocity of Uoo deflects upwards as shown in the figure above. Please answer the following questions, a) Define/show the forces acting on the flap with their correct directions. b) Is there a pressure difference between the fluid pressure acting on the top and bottom of the plate? If there is, which one is higher? c) If Gurney flap shown above is tilted more and more in order to deflect the incoming freestream flow more and more in the upwards direction, do you expect a flow reversal? If you do, why and where will that more likely to happen? d) What is the effect of these on the flow over the top rear of the car (shown below in red rectangle)? Explain. GURNEY FLAP U.
Force is a physical quantity that represents the interaction between two objects or systems. It is defined as the push or pull exerted on an object due to the interaction with another object or due to the presence of a field, such as gravitational or electromagnetic fields.
a) The forces acting on the Gurney flap are:
Lift force (L): The upward force exerted on the flap due to the deflection of the freestream flow. It acts perpendicular to the flow direction and opposes gravity.
Drag force (D): The resistance force acting parallel to the flow direction. It opposes the motion of the flap through the fluid.
Pressure forces: There are pressure forces acting on the top and bottom surfaces of the flap. These forces arise due to the difference in fluid pressure between the upper and lower surfaces of the flap.
b) Yes, there is a pressure difference between the fluid pressure acting on the top and bottom surfaces of the plate. The pressure on the bottom surface is higher than the pressure on the top surface. This pressure difference contributes to the generation of lift on the Gurney flap.
c) As the Gurney flap is tilted more to deflect the incoming freestream flow upward, a flow reversal is expected. The flow reversal occurs when the flow separates from the surface of the Gurney flap and changes its direction. This flow reversal is more likely to happen at the trailing edge of the Gurney flap, where the flow velocity is higher and the pressure is lower.
d) The effect of the Gurney flap on the flow over the top rear of the car is to create a region of high-pressure air above the flap. This high-pressure region helps to reduce the adverse pressure gradient and minimize flow separation. As a result, the flow over the top rear of the car remains attached for a longer distance, reducing drag and improving overall aerodynamic performance.
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A sheet of metal is illuminated by photons with a wavelength of 325 nm and the emitted electrons are found to have a maximum kinetic energy of 1.25 eV. If the same metal is illuminated by 225 nm light, what will be the speed of emitted electrons? Give your answer in km/s to 3 significant digits.
The speed of the emitted electrons when the metal is illuminated by 225 nm light is approximately 1.611 km/s.
To calculate the speed of emitted electrons, we can use the concept of the photoelectric effect and the equation for the kinetic energy of an electron:
K.E. = (1/2) * m * v^2
Where:
K.E. is the kinetic energy of the electron
m is the mass of the electron
v is the velocity of the electron
Given:
Wavelength of incident light (λ1) = 325 nm = 325 * 10^-9 m
Maximum kinetic energy (K.E.) = 1.25 eV
Wavelength of new incident light (λ2) = 225 nm = 225 * 10^-9 m
First, we need to find the energy of a photon using the equation:
E = hc / λ
Where:
E is the energy of a photon
h is Planck's constant (6.62607015 x 10^-34 J·s)
c is the speed of light (2.998 x 10^8 m/s)
λ is the wavelength of the light
For λ1:
E1 = (6.62607015 x 10^-34 J·s * 2.998 x 10^8 m/s) / (325 * 10^-9 m)
E1 ≈ 6.089 x 10^-19 J
For λ2:
E2 = (6.62607015 x 10^-34 J·s * 2.998 x 10^8 m/s) / (225 * 10^-9 m)
E2 ≈ 8.808 x 10^-19 J
Next, we can calculate the speed of the emitted electrons for the new wavelength using the equation:
K.E. = E - Φ
Where:
Φ is the work function of the metal (minimum energy required to release an electron)
Assuming the work function remains the same for the metal:
K.E. = E2 - Φ
Since K.E. = (1/2) * m * v^2, we can rearrange the equation to solve for v:
v = √((2 * K.E.) / m)
Given that the mass of an electron (m) is approximately 9.10938356 x 10^-31 kg, we can substitute the values:
v = √((2 * (8.808 x 10^-19 J - Φ)) / (9.10938356 x 10^-31 kg))
To find the value of Φ, we can use the given maximum kinetic energy for the incident light with λ1:
1.25 eV = 1.25 x 1.6 x 10^-19 J
So, Φ = 6.089 x 10^-19 J - 1.25 x 1.6 x 10^-19 J
Now, we can substitute the values and calculate the speed of the emitted electrons:
v = √((2 * (8.808 x 10^-19 J - (6.089 x 10^-19 J - 1.25 x 1.6 x 10^-19 J))) / (9.10938356 x 10^-31 kg))
v ≈ 1.611 x 10^6 m/s
Converting the speed to kilometers per second:
v ≈ 1.611 x 10^6 m/s * (1 km / 1000 m) * (1 s / 1000 ms)
v ≈ 1.611 km/s (to 3 significant digits)
Therefore, the speed of the emitted electrons when the metal is illuminated by 225 nm light is approximately 1.611 km/s.
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Which combination of units is equivalent to that used for force? Okg-m/s/s O kg⋅m-s² kg/(m/s²) O kg/m/s²
The unit of force is the newton (N), which is equivalent to kilogram-meter per second squared (kg⋅m/s²). It represents the product of mass and acceleration and is commonly used to quantify and describe forces.
The combination of units that is equivalent to the unit of force is the kilogram-meter per second squared (kg⋅m/s²), also known as the newton (N).
Force is a physical quantity that describes the interaction between two objects and their ability to change each other's motion.
In the International System of Units (SI), force is derived from the fundamental units of mass, length, and time.
The unit for mass is the kilogram (kg), which measures the amount of matter in an object. The unit for length is the meter (m), which measures the distance or displacement between two points.
The unit for time is the second (s), which measures the duration or interval of an event. When mass is multiplied by acceleration, which has units of meters per second squared (m/s²), the resulting unit is kg⋅m/s² or N.
The newton (N) is named after Sir Isaac Newton, a renowned physicist who made significant contributions to the study of forces and motion.
It is commonly used in various fields such as physics, engineering, and everyday life to quantify and describe forces acting on objects.
In summary, the correct combination of units equivalent to the unit of force is kg⋅m/s² or N, representing the product of mass and acceleration.
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true or false: destructive interference is the result of superposition of waves in phase.
False. Destructive interference is not the result of the superposition of waves in phase. Superposition is a term used to describe the phenomenon that occurs when two waves meet and combine to form a new wave.
The waveforms add together to create the new waveform, which has characteristics that are determined by the properties of the original waves.What is destructive interference?When waves meet and their waveforms are out of phase, destructive interference occurs. The amplitude of the resulting waveform is decreased, and the resulting waveform has a different shape than either of the original waveforms. Destructive interference, also known as out-of-phase interference, occurs when two waves meet and cancel each other out. When the waves are in phase, they combine to form a larger waveform with greater amplitude than either of the original waveforms. This is known as constructive interference.To conclude, destructive interference is not the result of the superposition of waves in phase. It occurs when two waves are out of phase and combine to create a new waveform that has a smaller amplitude than either of the original waveforms.
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Suppose that a sound source is emitting waves uniformly in all directions. If you move to a point twice as far away from the course, the frequency of the sound will be...?
The answer is unchanged. Can someone please show this through equations or explain why it remains unchanged? Don't just say doppler effect, please :)
If λ doubles, the frequency must remain constant, and this is why the frequency of the sound will be unchanged when you move twice as far away from the source.
What is Doppler Effect?
The Doppler Effect is an alteration in the apparent frequency of sound caused by the motion of the source, the observer, or both. The Doppler Effect may be used to calculate the relative speeds of the source and observer or to estimate the frequency of sound waves from a distant source, such as a star. The Doppler Effect is referred to as the shift in the frequency of the sound. Mathematically, this shift in frequency is referred to as the Doppler shift. Doppler shift in sound
The Doppler shift in sound may be computed using the following equation:
fD= v/c × f0
where v is the relative velocity of the observer and the source c is the velocity of sound waves in a given mediumf0 is the frequency of the source f D is the frequency observed Suppose that a sound source is emitting waves uniformly in all directions.
If we use the formula v = λ f
to calculate the frequency of sound, we get the following formula
:f = v/λ
Therefore, if λ doubles, the frequency must remain constant, and this is why the frequency of the sound will be unchanged when you move twice as far away from the source.
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what is the approximate thermal energy in kj/mol of molecules at 75 ° c?
Answer:
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To calculate the approximate thermal energy in kilojoules per mole (kJ/mol) of molecules at a given temperature, you can use the Boltzmann constant (k) and the ideal gas law.
The Boltzmann constant (k) is approximately equal to 8.314 J/(mol·K). To convert this to kilojoules per mole, we divide by 1000:
k = 8.314 J/(mol·K) = 0.008314 kJ/(mol·K)
Now, we need to convert the temperature to Kelvin (K) since the Boltzmann constant is defined in Kelvin. To convert from Celsius to Kelvin, we add 273.15 to the temperature:
T(K) = 75°C + 273.15 = 348.15 K
Finally, we can calculate the thermal energy using the formula:
Thermal energy = k * T
Thermal energy = 0.008314 kJ/(mol·K) * 348.15 K
Thermal energy ≈ 2.894 kJ/mol
Therefore, at 75°C, the approximate thermal energy of molecules is approximately 2.894 kilojoules per mole (kJ/mol).
The heat capacity of one mole of water is approximately 75.29/1000 = 0.07529 kj/mol. This value represents the approximate thermal energy in kj/mol of water molecules at 75 ° C.
Thermal energy refers to the energy present in a system that arises from the random movements of its atoms and molecules. When a body has a temperature of 75 ° C, it has a thermal energy that depends on the type of molecules in it and their specific heat capacity.
In this context, we will consider the thermal energy in kj/mol of molecules at 75 ° C.Let's use water as an example to calculate the approximate thermal energy in kj/mol of molecules at 75 ° C. The specific heat capacity of water is 4.18 J/g °C, and the molar mass of water is 18.01528 g/mol. Therefore, the thermal energy in kj/mol of water molecules at 75 ° C can be calculated as follows:ΔH = mcΔt, whereΔH = thermal energy,m = mass of the sample,c = specific heat capacity of the sample,Δt = change in temperature
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the intensity of an em wave is 10 w/m2. what will the intensity be if the amplitude of the electric field is doubled?
The new intensity is 4 times the original value. Thus, if the intensity of the em wave was initially 10 W/m², it will be 40 W/m² when the amplitude of the electric field is doubled.
The intensity of an em wave is given as 10 W/m². If the amplitude of the electric field is doubled, the new intensity will be 4 times the original value. Hence, the intensity of the em wave will be 40 W/m².An electromagnetic wave consists of two perpendicular and transverse oscillations which are the electric field and magnetic field respectively. The two fields are perpendicular to the direction of propagation of the wave which means they are both oscillating in a plane perpendicular to the wave’s direction of travel.
The intensity of an electromagnetic wave is proportional to the square of its electric field amplitude. The formula to calculate the intensity is given as;I = E²/2μ where;I = IntensityE = Electric field amplitudeμ = Permeability of free space .
When the amplitude of the electric field is doubled, it means that the new amplitude is twice the original value. Thus, the new intensity can be calculated as follows; E_new = 2E_old Substituting the above value into the formula for intensity gives; I_new = (2E_old)²/2μ = 4(E_old²/2μ) = 4I_old .
Therefore, the new intensity is 4 times the original value. Thus, if the intensity of the em wave was initially 10 W/m², it will be 40 W/m² when the amplitude of the electric field is doubled.
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when a p = 680 w ideal (lossless) transformer is operated at full power with an rms input current of i1 = 3.5 a, it produces an rms output voltage of v2 = 8.1 v.
The rms input voltage to the transformer is 680/3.5 = 194.3 volts.
According to the question, the transformer is ideal (lossless), which means that there are no losses that occur in the transformer.
As a result, the input power is equal to the output power, and the voltage and current relationship between the input and output of the transformer is proportional.
In an ideal transformer, we use the following equations to calculate the output voltage and input voltage, respectively:
V₁ / V₂ = N₁ / N₂
I₁ / I₂ = N₂ / N₁
Where V₁ is the input voltage, V₂ is the output voltage, I₁ is the input current, I₂ is the output current, N₁ is the number of turns on the primary side, and N₂ is the number of turns on the secondary side of the transformer.
Now we can use these equations to find the input voltage of the transformer when the output voltage is 8.1 V and the power rating of the transformer is 680 W. Rearranging the equation for power, we get:
P = V₁ I₁ = V₂ I₂
Where P is the power, and substituting the values given in the question we have:
680 = V₁ × 3.5V₁ = 680 / 3.5V₁ = 194.3V
Therefore, the rms input voltage to the transformer is 194.3 volts.
The rms input voltage to the transformer is 194.3 volts.
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how can humans avoid the possible damaging effects of nanotechnology?
Nanotechnology is a rapidly expanding field with a wide range of applications, from medicine and electronics to energy and manufacturing. While the possibilities of nanotechnology are vast, there are potential risks associated with it, such as toxicity, environmental impact, and unintended consequences.
Here are some ways in which humans can avoid the possible damaging effects of nanotechnology:1. Regulation: Governments should put regulations in place to control the use and development of nanotechnology. These regulations should include safety standards and ethical guidelines for the research and development of nanotechnology.
2. Research: Researchers should conduct studies to determine the potential risks of nanotechnology and ways to minimize them. This research should include toxicology studies, environmental impact assessments, and assessments of unintended consequences.
3. Education: Educating the public about the potential risks of nanotechnology is essential. The public should be aware of the potential risks and how to protect themselves.
4. Proper use: The proper use of nanotechnology can also minimize the potential risks associated with it. For example, nanoparticles used in consumer products should be designed to minimize toxicity and should be used only when necessary.5. Disposal: The proper disposal of nanomaterials is also important to minimize the potential risks. Nanomaterials should be disposed of in a manner that minimizes their impact on the environment and human health.
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Negative charge −Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin.
Find the x-component of the net electric field at the origin.
Find the y-component of the net electric field at the origin.
The y-component of the net electric field at the origin is given by:E_y = (kQ/a²) sin θwhere Q is the total charge of the quarter circle, a is the radius, k is Coulomb's constant, and θ is the angle between the x-axis and the line connecting the origin and the element.
Given information: Negative charge −Q is distributed uniformly around a quarter-circle of radius a that lies in the first quadrant, with the center of curvature at the origin.
To determine the x-component of the net electric field at the origin, we can break down the quarter circle into infinitesimally small charge elements. By taking the electric field due to each infinitesimal element, we can calculate the net electric field due to the entire quarter circle at the origin. The x-component of the net electric field at the origin is given by:E_x = (kQ/a²) cos θwhere Q is the total charge of the quarter circle, a is the radius, k is Coulomb's constant, and θ is the angle between the x-axis and the line connecting the origin and the element.
To determine the y-component of the net electric field at the origin, we can similarly break down the quarter circle into infinitesimally small charge elements. By taking the electric field due to each infinitesimal element, we can calculate the net electric field due to the entire quarter circle at the origin. The y-component of the net electric field at the origin is given by:E_y = (kQ/a²) sin θwhere Q is the total charge of the quarter circle, a is the radius, k is Coulomb's constant, and θ is the angle between the x-axis and the line connecting the origin and the element.
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Four very long current-carrying wires in the same plane intersect to form a square 50.0 cm on each side, as shown in Figure 3. 1. 1 =10.0 A 14 12=8.00 A 13 =20.0 A Figure 3
(a) Determine the magnitude and direction of the magnetic field produced by each current Lland ts at the center of the square.
(b) Determine the magnitude and direction of the current, 14 in the right vertical wire if the resultant magnetic field produced by all four wires at the center of the square is zero.
(a) The magnetic field produced by each current at the center of the square can be determined using the formula for the magnetic field produced by a long straight wire.
The magnitude of the magnetic field produced by each wire can be calculated using the equation:
B = (μ₀ * I) / (2 * π * r)
where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the wire to the center of the square. Since all four wires are in the same plane and intersect to form a square, the magnetic field produced by each wire will have the same magnitude and direction. The direction of the magnetic field can be determined using the right-hand rule, where the thumb points in the direction of the current and the curled fingers give the direction of the magnetic field.
(b) To determine the magnitude and direction of the current 14 in the right vertical wire, we need to ensure that the resultant magnetic field produced by all four wires at the center of the square is zero.
Since the magnetic fields produced by wires 1, 2, and 3 are known, we can use vector addition to find the magnitude and direction of the current 14 that will cancel out the net magnetic field. By adding the magnetic fields produced by each wire and setting the resultant field to zero, we can solve for the magnitude and direction of the current 14 in the right vertical wire.
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what is the rms value of the electric field in a sinusoidal electromagnetic wave that has a maximum electric field of 67 v/m ?
The rms value of the electric field in the sinusoidal electromagnetic wave is approximately 47.4 V/m.
The root mean square (rms) value of the electric field in a sinusoidal electromagnetic wave can be calculated using the following formula:
E_rms = E_max / √2
where E_max is the maximum electric field.
Given that the maximum electric field is 67 V/m, we can plug this value into the formula to find the rms value:
E_rms = 67 V/m / √2 ≈ 47.4 V/m
Therefore, the rms value of the electric field in the sinusoidal electromagnetic wave is approximately 47.4 V/m.
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4 batteries of emf 2 V and internal resistance 4 each in parallel are connected to the external resistance 3. The power liberated by the external resistance is: O A. 0.75 W B. 0.4 W C. 40 W D. 220 mW E. None of the above QUESTION 3 The circuit parameters are as follows R1=1 12, R2=5 and the ideal (zero internal resistance) batteries of emfs E1=E2=E3=8 V each. Find the current through the battery E3.
The power liberated by external resistance will be 0.75W. option A is correct. The magnitude of the current through E₃ is 16/3A.
When batteries are connected in parallel, the total EMF remains the same while the internal resistances add up reciprocally. Therefore, the equivalent EMF of the parallel combination is also 2V, and the equivalent internal resistance is 1Ω (1/R_eq = 1/4 + 1/4 + 1/4 + 1/4 = 1).
Using Ohm's Law, the current flowing through the circuit is given by I = E_eq / (R + r_eq), where E_eq is the equivalent emf, R is the external resistance, and r_eq is the equivalent internal resistance.
Given E_eq = 2V and R = 3Ω, we have;
I = 2V / (3Ω + 1Ω) = 2V / 4Ω = 0.5A
The power liberated by the external resistance can be calculated using the formula P = I² × R, where I is the current and R is the resistance.
P = (0.5A)² × 3Ω = 0.25W × 3Ω = 0.75W
Therefore, the power liberated by the external resistance is 0.75W
Hence, A. is the correct option.
Since the batteries are ideal with zero internal resistance, the current through each battery will depend only on the external resistances connected in the circuit.
To find the current through battery E3, we can analyze the circuit using Ohm's Law and Kirchhoff's Laws.
Using Kirchhoff's Voltage Law (KVL) in the loop containing E₃, R₁, and R₂, we have:
-E₁ + I₁R₁ + I₂R₂ + E₃ = 0
Since E₁ = E₂ = E₃ = 8V and R₁ = 1Ω, R₂ = 5Ω, we can rewrite the equation as:
-8V + I11Ω + I25Ω + 8V = 0
Simplifying the equation, we have:
I₁ + 5I₂ = 0
We also know that the total current entering the node containing E₃ is equal to the current leaving the node. Therefore, I₃ = I₁ + I₂.
Substituting the value of I₁ from the previous equation, we get:
I₃ = -5I₂ + I₂ = -4I₂
Since we are interested in finding the current through battery E₃, which is I₃, we need to determine the value of I₂.
To find I₂, we can use Ohm's Law in the loop containing R₁, R₂, and E₂:
I₂ = E₂ / (R₁ + R₂) = 8V / (1Ω + 5Ω) = 8V / 6Ω = 4/3A
Finally, substituting the value of I₂ back into the equation for I₃, we get:
I₃ = -4 × (4/3)A = -16/3A
The negative sign indicates that the current through battery E₃ is in the opposite direction to our assumed direction. Therefore, the magnitude of the current through E₃ is 16/3A.
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