Circuits
•
Resistor Circuits.
We’ll look at more
complex circuits this
week.
•
Capacitor Circuits.
Adding a capacitor to a
resistor circuit allows for
timing functions.
•
Electricity in the
Body. The physics of
resistor-capacitor circuits
can be used to explain
signal propagation in the
nervous system.
Reducing Complex Circuits, Part I
Rage Against the
Dying of the
Light.
Holiday lights use
simple series circuits
so that the bulbs can
be low voltage.
Suppose there are 50
bulbs in one string.
What is the voltage
across each bulb?
How does the string stay lit
when one bulb goes out?
Reducing Complex Circuits, Part II
What’s the Voltage?
The diagram below shows a circuit with two batteries
and three resistors. What is the potential difference
across the 200 Ω resistor?
Understanding Circuits
a. Which bulb is brightest?
b. Which bulb is dimmest?
Ideal Wires,
Ideal Batteries,
Light Bulbs are
Resistors
Suppose a wire is connected between points 1 and 2.
Does the brightness of each bulb:
! A. !Increase
! B. !Decrease
Understanding Circuits
a. Which bulb is brightest?
b. Which bulb is dimmest?
Voltage
Is,
Current
Flows.
Suppose a wire is connected between points 1 and 2.
Does the brightness of each bulb:
! A. !Increase
! B. !Decrease
What’s The Current?
The diagram below shows a segment of a circuit. What is
the current in the 200 Ω resistor?
What’s the Voltage?
The diagram below shows a circuit with two batteries
and three resistors. What is the potential difference
across the 200 Ω resistor?
What’s the Resistance?
There is a current of 1.0 A in the circuit below.
What is the resistance of the unknown circuit element?
What’s the Current?
What is the current supplied by the battery in the
following circuit?
Which is quicker?
Series
Parallel
Explain which wiring will result in quicker cooking, and why.
You must use a mathematical relationship.
Common Combinations
−1
Requivalent = R1 + R2 = 2R
Requivalent
⎡1
1 ⎤
R
=⎢ + ⎥ =
2
⎣ R1 R2 ⎦
Simplifying Circuits
What is the equivalent resistance of the following circuit?
Measuring Voltage and Current
Ammeter:
Measures current.
R=0 Ω; no voltage.
What is the value of R?
Voltmeter: Measures
potential difference.
R=∞ Ω; no current.
What is the value of I?
What is the value of R?
Circuits Calculations.
What is the current provided by the battery in the
following circuit?
Circuits Calculations.
What is the current through each of the resistors in the
following circuit?
Voltage is. Current flows.
1)Which point,
a or b, is at a
higher
potential?
2.0 Ω
1.0 Ω
1.0 Ω
2.0 Ω
3.0 V
2)What is the potential difference Vab?
Grand Finale.
What is the current through each of the resistors in the
following circuit?
Warming Up.
the figure.
Warming Up.
What’s the potential at the
the figure.
noted point in the circuit?
!
!
!
!
A. !
B. !!
C. !
D. !
10 V
6V
5V
4V
Warming Up: What are the two resistors?
What are the resistances of the two unknown resistors
in this circuit?
R1
R2
Warming Up.
What is the value of resistor R in the figure?
Unfinished Business.
What is the current through each of the resistors in the
following circuit?
Capacitor formulas
Unit: farad, F:
Storing Charge
1)What is the capacitance of the 2 l bottle Leyden jar
capacitors we use in class?
2)The capacitor is charged up to 10,000 V, then discharges
in 0.01 s. What is the current?
Area: ! ! !
Thickness: !!
κ:!! ! ! !
ε0:!! ! ! !
0.08 m2
0.00025 m
2.8
8.85x10-12 C2/N•m2
Capacitors in series and in parallel
Which of the following combinations of capacitors has:
! 1) the highest capacitance?
! 2) the lowest capacitance?
Capacitor Discharge
11 11
C
11 11
C
R
22 22
22 22
I
R
C
I
2 2
R
DVC
(DVC)0
I0
0
1 1
I0
t
t50
0
t
t50
Voltage, current decrease with time.
Capacitor Discharge
DVC
(DVC)0
0.37(DVC)0
0.13(DVC)0
0
0
t
2t
τ = RC
3t
ΔVC = ( ΔVC )0 e−t /τ
t
Timing Circuits
DVC
t
Intermittent Wipers
Rotating the dial changes a variable resistor. Does turning
the dial toward “F” increase or decrease the resistance?
Half life:
t1 2 = τ ln 2
RC Timing
The following circuits contain capacitors charged to 5.0 V. All of
the switches are closed at the same time.
After 1 second has passed, which capacitor has the highest
voltage? The lowest?
RC Timing
A 10 µF capacitor is initially charged to 20 µC. The
capacitor is discharged through a 1.0 kΩ resistor.
How long does it take to reduce the capacitor’s
charge to 10 µC?
Large Current, Short Pulse
A typical defibrillator has a 32 µF capacitor charged to
5000 V. The electrodes connected to the patient are
coated with a conducting gel that reduces the resistance
of the skin so that the effective resistance of the patient’s
torso is100 Ω.
a. What is the current at the instant the switch is
closed?
b. What is the current 5.0 ms after the switch is
closed?