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0. Math Review31m
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  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

27. Resistors & DC Circuits

Solving Resistor Circuits

Physics

27. Resistors & DC Circuits

Solving Resistor Circuits

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Problem 20

Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]

(II) A power supply has a fixed output voltage of 12.0 V, but you need V_T = 3.0 V output for an experiment. (a) Using the voltage divider shown in Fig. 26–47, what should R₂ be if R₁ is 16.5 Ω? (b) What will the terminal voltage V_T be if you connect a load to the 3.0-V output, assuming the load has a resistance of 7.0Ω?

Verified step by step guidance

Step 1: Understand the voltage divider circuit. The voltage divider uses two resistors, R₁ and R₂, connected in series across a voltage source. The output voltage VT is taken across R₂. The formula for VT is given by:

V_{T} = V_{in} \times \frac{R_{2}}{R_{1} + R_{2}}

, where Vin is the input voltage.

Step 2: For part (a), substitute the given values into the voltage divider formula. Vin = 12.0 V, VT = 3.0 V, and R₁ = 16.5 Ω. Rearrange the formula to solve for R₂:

R_{2} = R_{1} \times \frac{V_{T}}{V_{in} - V_{T}}

. Plug in the values to find R₂.

Step 3: For part (b), when a load resistance RL = 7.0 Ω is connected in parallel with R₂, the effective resistance of R₂ changes. Use the formula for parallel resistances:

R_{eff} = \frac{R_{2} \times R_{L}}{R_{2} + R_{L}}

. Calculate the effective resistance of R₂.

Step 4: Substitute the effective resistance of R₂ (Reff) back into the voltage divider formula:

V_{T} = V_{in} \times \frac{R_{eff}}{R_{1} + R_{eff}}

. This will give the new terminal voltage VT.

Step 5: Verify your calculations and ensure that the values make sense physically. The terminal voltage VT should decrease when the load is connected, as the effective resistance of R₂ decreases, causing a redistribution of the voltage.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Voltage Divider Rule

The voltage divider rule is a fundamental principle in electrical engineering that describes how voltage is distributed across resistors in a series circuit. According to this rule, the output voltage across a resistor in series is a fraction of the total voltage, determined by the ratio of that resistor's resistance to the total resistance. This concept is crucial for calculating the desired output voltage (V_T) in the given circuit.

Ohm's Law

Ohm's Law is a basic principle in electronics that relates voltage (V), current (I), and resistance (R) in a circuit, expressed as V = I × R. This law is essential for understanding how changes in resistance affect current flow and voltage across components. In this problem, it helps in analyzing the impact of the load resistance on the terminal voltage when connected to the output.

Equivalent Resistance

Equivalent resistance is the total resistance of a circuit or a portion of a circuit, which can be calculated by combining resistors in series and parallel. In this scenario, understanding how to find the equivalent resistance of R1 and R2 is vital for determining the overall behavior of the circuit, especially when a load is connected, as it influences the voltage drop and current distribution.

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Related Practice

Textbook Question

(II) Suppose two batteries, with unequal emfs of 2.00 V and 3.00 V, are connected as shown in Fig. 26–63. If each internal resistance is r = 0.350Ω and R = 4.00Ω, what is the voltage across the resistor R?

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Textbook Question

(III) (a) Determine the currents I₁, I₂, and I₃ in Fig. 26–58. Assume the internal resistance of each battery is r = 1.0 Ω.

(b) What is the terminal voltage of the 6.0-V battery?

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Textbook Question

The circuit shown in Fig. 26–89 is a primitive 4-bit digital-to-analog converter (DAC). In this circuit, to represent each digit (2ⁿ) of a binary number, a “1” has the nᵗʰ switch closed whereas zero (“0”) has the switch open. For example, 0010 is represented by closing switch n = 1, while all other switches are open. Show that the voltage V across the 1.0 - Ω resistor for the binary numbers 0001, 0010, 0100, and 1010 (which represent 1, 2, 4, 10) follows the pattern that you expect for a 4-bit DAC.

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Textbook Question

(II) (a) What is the potential difference between points a and d in Fig. 26–55 (similar to Fig. 26–12, Example 26–8), and (b) what is the terminal voltage of each battery?

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Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]

(II) What is the net resistance of the circuit connected to the battery in Fig. 26–46?

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Textbook Question

(III) Determine the net resistance in Fig. 26–61 (a) between points a and c, and (b) between points a and b. Assume R' ≠ R. [Hint: Apply an emf between the two points in each case and determine currents; use symmetry at junctions.]

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Textbook Question

Consider two unequal resistors, of resistance R₁ and R₂, that are connected either in series or in parallel. Fill in the Table below assuming the electric potential on the low-voltage end of the combination is V_A volts and the potential at the high-voltage end of the combination is V_B volts. First draw diagrams.

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Textbook Question

Measurements made on circuits that contain large resistances can be confusing. Consider a circuit powered by a battery ε = 15.000 V with a 10.00-MΩ resistor in series with an unknown resistor R. As shown in Fig. 26–92, a particular voltmeter reads V₁ = 366 mV when connected across the 10.00 -MΩ resistor and this meter reads V₂ = 7.317 V when connected across R. Determine the value of R. [Hint: Define R_V as the voltmeter’s internal resistance.]

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