Table of contents

0. Math Review31m
- Math Review
  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

Previous problemNext problem

Problem 70b

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.

Verified step by step guidance

Step 1: Understand the physical setup of the problem. Two metal plates are charged to ±12.5 nC and connected by a copper wire. The plates act as a capacitor, and the wire provides a path for the charges to flow, creating a current. The question asks about the behavior of this current over time.

Step 2: Recall the concept of a discharging capacitor. When a capacitor is connected through a conductor, the charges on the plates flow to neutralize each other. The current is initially high because the potential difference between the plates is large, but it decreases over time as the charge on the plates diminishes.

Step 3: Use the formula for the current in a discharging capacitor: \( I(t) = I_0 e^{-t/RC} \), where \( I_0 \) is the initial current, \( R \) is the resistance of the wire, \( C \) is the capacitance of the plates, and \( t \) is time. This equation shows that the current decreases exponentially with time.

Step 4: Consider the physical properties of the wire and plates. The resistance \( R \) of the copper wire can be calculated using \( R = \frac{\rho L}{A} \), where \( \rho \) is the resistivity of copper, \( L \) is the length of the wire, and \( A \) is its cross-sectional area. The capacitance \( C \) of the plates can be calculated using \( C = \frac{\varepsilon_0 A}{d} \), where \( \varepsilon_0 \) is the permittivity of free space, \( A \) is the area of the plates, and \( d \) is the separation between them.

Step 5: Conclude that the current decreases with time. This is because the charge on the plates diminishes as the capacitor discharges, reducing the potential difference and, consequently, the current flowing through the wire. The exponential decay behavior is characteristic of a discharging capacitor.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Play a video:

Was this helpful?

Key Concepts

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

Capacitance

Capacitance is the ability of a system to store electric charge per unit voltage. In this scenario, the two metal plates form a capacitor, where the capacitance depends on their area and the distance between them. When charged, the plates create an electric field, and the stored energy can influence the current flow when they are connected.

Current Flow in Circuits

Current is the flow of electric charge through a conductor, measured in amperes. When the charged plates are connected by a wire, the potential difference between them drives the current. The behavior of the current over time is influenced by the capacitance of the plates and the resistance of the wire, which can cause the current to change as the system reaches equilibrium.

RC Time Constant

The RC time constant is a measure of the time it takes for the current to charge or discharge in a resistor-capacitor circuit. It is calculated as the product of resistance (R) and capacitance (C). In this case, as the plates discharge through the wire, the current will initially be high and then decrease over time, following an exponential decay governed by the RC time constant.

Watch next

Master Solving Resistor Circuits with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

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?

views

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.

views

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?

views

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?

views

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?

views

Multiple Choice

What is current and voltage across each resistor below?

What is the voltage of the battery below?

1191

views

rank