At t = 0, the open switch in Figure P31.46 is thrown closed. We wish to find a symbolic expression for the current in the inductor for time t > 0. Let this current be called i and choose it to be downward in the inductor in Figure P31.46. Identify i1 as the current to the right through R1 and i2 as the current downward through R2. (a) Use Kirchhoff’s junction rule to find a relation among the three currents. (b) Use Kirchhoff’s loop rule around the left loop to find another relationship. (c) Use Kirchhoff’s loop rule around the outer loop to find a third relationship. (d) Eliminate i1 and i2 among the three equations to find an equation involving only the current i. (e) Compare the equation in part (d) with Equation 31.6 in the text. Use this comparison to rewrite Equation 31.7 in the text for the situation in this problem and show that
where R′ = R1R2/(R1 + R2).
Figure P31.46
(a)
Answer to Problem 32.70AP
Explanation of Solution
Given info: The figure that shows the given circuit is shown below.
Figure (I)
According to Kirchhoff’s junction rule, the total incoming currents are equal to the total outgoing currents at a junction.
From the circuit diagram equating the incoming currents to the outgoing current,
Here,
Conclusion:
Therefore, the relation among three currents by Kirchhoff’s junction rule are
(b)
Answer to Problem 32.70AP
Explanation of Solution
Given info: The figure that shows the given circuit is shown in figure (I).
According to Kirchhoff’s loop rule, the sum of all the voltage across all the elements in a loop must be zero.
From the circuit diagram equating the voltage across the elements in the left loop is equal to zero.
Here,
Conclusion:
Therefore, the relationship between the given variables around the left loop by Kirchhoff’s loop rule is
(c)
Answer to Problem 32.70AP
Explanation of Solution
Given info: The figure that shows the given circuit is shown in figure (I).
According to Kirchhoff’s loop rule, the sum of all the voltage across all the elements in a loop must be zero.
From the circuit diagram equating the voltage across the elements in the outer loop is equal to zero.
Conclusion:
Therefore, the relationship between the given variables around the outer loop by Kirchhoff’s loop rule is
(d)
Answer to Problem 32.70AP
Explanation of Solution
Given info: The figure that shows the given circuit is shown in figure (I).
From equation (1), the expression for the
Substitute
From equation (2), the expression for the
Substitute
Equate equation (3) and equation (4) for
Further solve the above equation,
Assume
Substitute
Thus, the require equation in term of current
Conclusion:
Therefore, the equation that involve only current
(e)
Answer to Problem 32.70AP
Explanation of Solution
From the textbook the equation
From the part (d), the equation is given as,
Since both the equation shown above are same therefore their solution are also same.
The solution of the equation
Similarly rewrite the equation
Substitute
Conclusion:
Therefore, the equation
Want to see more full solutions like this?
Chapter 32 Solutions
Physics for Scientists and Engineers (AP Edition)
- No chatgpt pls will upvotearrow_forwardair is pushed steadily though a forced air pipe at a steady speed of 4.0 m/s. the pipe measures 56 cm by 22 cm. how fast will air move though a narrower portion of the pipe that is also rectangular and measures 32 cm by 22 cmarrow_forwardNo chatgpt pls will upvotearrow_forward
- 13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…arrow_forwardNo chatgpt pls will upvotearrow_forwarda cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?arrow_forward
- Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were: 222.22 800.00 61.11 641.67 0.00 588.89 11.11 588.89 8.33 588.89 11.11 588.89 5.56 586.11 2.78 583.33 Give in the answer window the calculated repeated experiment variance in m/s2.arrow_forwardNo chatgpt pls will upvotearrow_forwardCan you help me solve the questions pleasearrow_forward
- Can you help me solve these questions please so i can see how to do itarrow_forwardHow can i solve this if n1 (refractive index of gas) and n2 (refractive index of plastic) is not known. And the brewsters angle isn't knownarrow_forward2. Consider the situation described in problem 1 where light emerges horizontally from ground level. Take k = 0.0020 m' and no = 1.0001 and find at which horizontal distance, x, the ray reaches a height of y = 1.5 m.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning