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0. Math Review31m
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1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
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5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
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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 69

Textbook Question

A 150 μF defibrillator capacitor is charged to 1500 V. When fired through a patient’s chest, it loses 95% of its charge in 40 ms. What is the resistance of the patient’s chest?

Verified step by step guidance

Step 1: Recognize that the capacitor discharges through the patient's chest, which can be modeled as an RC circuit. The voltage across the capacitor during discharge follows the equation:

V_{t} = V_{0} e^{- \frac{t}{τ}}

, where

τ

is the time constant of the circuit.

Step 2: The time constant

τ

is given by the formula:

τ = R C

, where

R

is the resistance and

C

is the capacitance.

Step 3: Use the information that the capacitor loses 95% of its charge in 40 ms. This means the voltage drops to 5% of its initial value. Substitute this into the discharge equation:

V_{t} = V_{0} e^{- \frac{t}{τ}}

, where

V_{t} = 0.05 V_{0}

and

t = 40 ms

Step 4: Solve for the time constant

τ

using the equation:

e^{- \frac{t}{τ}} = 0.05

. Take the natural logarithm of both sides to isolate

\frac{t}{τ}

- \frac{t}{τ} = \ln (0.05)

. Rearrange to find

τ

τ = \frac{t}{-}

Step 5: Once

τ

is calculated, use the formula

τ = R C

to solve for the resistance

R

. Substitute the given capacitance

C = 150 μ F

and the calculated value of

τ

into the equation to find

R

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Key Concepts

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

Capacitance

Capacitance is the ability of a capacitor to store electrical charge per unit voltage. It is measured in farads (F), and in this case, the defibrillator capacitor has a capacitance of 150 μF (microfarads). The charge (Q) stored in a capacitor can be calculated using the formula Q = C × V, where C is capacitance and V is voltage.

Exponential Decay of Charge

When a capacitor discharges through a resistor, the charge decreases exponentially over time. The relationship is described by the equation Q(t) = Q0 * e^(-t/RC), where Q0 is the initial charge, R is resistance, and C is capacitance. In this scenario, the capacitor loses 95% of its charge in 40 ms, which can be used to find the resistance of the patient's chest.

Ohm's Law

Ohm's Law relates voltage (V), current (I), and resistance (R) in an electrical circuit, expressed as V = I × R. In the context of the defibrillator, understanding this relationship is crucial for calculating the resistance of the patient's chest based on the current flowing through it as the capacitor discharges. This law helps in determining how the resistance affects the rate of charge loss.

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Related Practice

Textbook Question

A 300 μF capacitor is charged to 9.0 V, then connected in parallel with a 5000 Ω resistor. The capacitor will discharge because the resistor provides a conducting pathway between the capacitor plates, but much more slowly than if the plates were connected by a wire. Let t=0 s be the instant the fully charged capacitor is first connected to the resistor. At what time has the capacitor voltage decreased by half, to 4.5 V?

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Textbook Question

What is the time constant for the discharge of the capacitors in FIGURE EX28.34?

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Textbook Question

The capacitor in an RC circuit is discharged with a time constant of 10 ms. At what time after the discharge begins are (a) the charge on the capacitor reduced to half its initial value and (b) the energy stored in the capacitor reduced to half its initial value?

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Textbook Question

A circuit you’re using discharges a 20 μF capacitor through an unknown resistor. After charging the capacitor, you close a switch at t = 0 s and then monitor the resistor current with an ammeter. Your data are as follows: Use an appropriate graph of the data to determine (a) the resistance and (b) the initial capacitor voltage.

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Textbook Question

A 15 μF capacitor charged to 12 V is discharged through a resistor. The energy stored in the capacitor decreases by 50% in 0.25 s. What is the value of the resistance?

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Textbook Question

Two 10-cm-diameter metal plates 1.0 cm apart are charged to ±12.5 nC. They are suddenly connected together by a 0.224-mm-diameter copper wire stretched taut from the center of one plate to the center of the other. Does the current increase with time, decrease with time, or remain steady? Explain.

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Textbook Question

You’ve made the finals of the Science Olympics! As one of your tasks, you’re given 1.0 g of aluminum and asked to make a wire, using all the aluminum, that will dissipate 7.5 W when connected to a 1.5 V battery. What length and diameter will you choose for your wire?

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Multiple Choice

What is current and voltage across each resistor below?

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