RC Circuits. Lecture 13. Chapter 31. Physics II. Course website:

Size: px

Start display at page:

Download "RC Circuits. Lecture 13. Chapter 31. Physics II. Course website:"

Elinor Ball
6 years ago
Views:

1 Lecture 13 Chapter 31 Physics II RC Circuits Course website: Lecture Capture:

2 Steady current Time-varying current In the preceding sections we dealt with circuits in which the circuits elements were resistors and in which the currents did not vary with time. Here we introduce the capacitor as a circuit element, which will lead us to the study of time-varying currents.

3 RC circuit (Charging a Capacitor) Now, we know Kirchhoff s rules and let s apply them to study an RC circuit

Let s look at the circuit at some arbitrary moment of time t and apply Kirchhoff s loop rule: + + 0 0 There are two variables I(t),Q(t), which

4 The capacitor charge at time t is: Charging a Capacitor The figure shows an RC circuit, some time after the switch was closed. We need to analyze it:,,? Let s look at the circuit at some arbitrary moment of time t and apply Kirchhoff s loop rule: There are two variables I(t),Q(t), which are dependent: (The resistor current is the rate at which charge is added to the capacitor) / 0 It is not hard to solve, but we just present the solution (see the solution at the end of this presentation) 0 denote RC (the time constant) and (full charge of the capacitor) 1 1

Resistor Current and Capacitor Voltage Let s

looks like The Land Run of 1893 (the Oklahoma

Electrons waiting for a switch to be closed.

5 Resistor Current and Capacitor Voltage Let s calculate the resistor current: RC This current looks like The Land Run of 1893 (the Oklahoma Territory) shown in the movie Far and Away ( No current. Electrons waiting for a switch to be closed. 1 Race begins. Electrons are on the way to their lands. The first photo of a traveling electron

6 ConcepTest RC circuit 1 In the circuit shown, the capacitor is originally uncharged. Describe the behavior of the lightbulb from the instant switch S is closed until a long time later. A) No light. B) First, it is bright, then dim. C) First, it is dim, then bright. D) Steady bright. When the switch is first closed, the current is high and the bulb burns brightly. As the capacitor charges, The voltage across the capacitor increases causing the current to be reduced, and the bulb dims.

7 RC circuit (discharging) We want to analyze the RC circuit:,,? At t = 0, the switch closes and the charged capacitor begins to discharge through the resistor.

8 RC circuit (discharging) The figure shows an RC circuit, some time after the switch was closed. Kirchhoff s loop law applied to this circuit clockwise is: Q and I in this equation are the instantaneous values of the capacitor charge and the resistor current. The resistor current 0, The resistor current is the rate at which charge is removed from the capacitor: ln 0 denote time constant as: where Q 0 is the charge at t = 0 The charge on the capacitor of an RC circuit

9 RC circuit (discharging) Let s plot it:

calculate the voltage of the capacitor: 2.7 0.

10 RC circuit (discharging) Let s calculate the resistor current: I 0 is the initial current The current undergoes the same exponential decay Let s calculate the voltage of the capacitor: / / the voltage across the capacitor Now we know everything about the circuit [Q(t), I(t), and ΔV(t)]

11 ConcepTest RC circuit 1 Which capacitor discharges more quickly after the switch is closed? time constant = RC = 12 µs = 15 µs So the capacitor A discharges faster than B A) Capacitor A. B) Capacitor B. C) They discharge at the same rate. D) Can t say without knowing the initial amount of charge.

12 ConcepTest RC circuit 3 What is the time constant for the discharge of the capacitor shown in the figure? A) 5 s B) 4 s C) 2 s D) 1 s E) The capacitor does not discharge because the resistors cancel each other += time constant by definition = R eq C How about this? = R eq C=4Ωx1F=4 seconds = R eq C eq

13 ConcepTest RC circuit 2 Figure shows the voltage as a function of time of a capacitor as it is discharged (separately) through three different resistors. Rank in order, from largest to smallest, the A) R 1 < R 2 < R 3 B) R 1 < R 3 < R 2. C) R 2 < R 3 < R 1. D) Not enough information. values of the resistances R 1, R 2, and R 3. time constant by definition = RC From the figure we can see that: <...

14 I used an RC circuit in my paper. My application Charging a Capacitor Discharging a Capacitor

15 What you should read Chapter 31 (Knight) Sections 31.9

16 Derivation (charging a capacitor)

17 Thank you See you on Tuesday

18 ConcepTest Wheatstone Bridge An ammeter A is connected A) l between points a and b in the B) l/2 circuit below, in which the four C) l/3 resistors are identical. The current D) l/4 through the ammeter is: E) zero Since all resistors are identical, the voltage drops are the same across the upper branch and the lower branch. Thus, the potentials at points a and b are also the same. Therefore, no current flows. V I

Lecture 12 Chapter 28 RC Circuits Course website:

Lecture 12 Chapter 28 RC Circuits Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 28: Section 28.9 RC circuits Steady current Time-varying