Download Chapter 29 Emf and Circuits

Chapter 29 Emf and Circuits
第二十九章 電動勢與電路
Emf devices
An emf device is a charge
pump that can maintain a
potential difference
between a pair of
terminals.
Emf devices include
battery, electric generator,
solar cell, fuel cell, and
thermopile. Physiological
emf devices include
electric eel, human being,
and some plants.
Work, energy, and emf
The emf of an emf device is
defined to be the work per
unit charge that the device
does in moving charge
from its low-potential
terminal (-) to its highpotential terminal (+).
E
dW
dq
An ideal emf device versus a real
emf device
Resistance in series
V  IR1  IR2  I ( R1  R2 )
Power
Power of the emf device is:
Pemf  iE
Power transferred out is:
P  I (E  Ir )  Pemf  Pr
Pr  I 2 r
E
I
rR
E2
E2 r
P

r  R ( r  R) 2
Sample problem 1
The emfs and resistances in the
circuit have the following values:
E1 = 4.4 V, E2 = 2.1 V, r1 = 2.3 ,
r2 = 1.8 , R = 5.5 . (a) What is
the current i in the circuit? (b)
What is the potential difference
between the terminals of battery
1?
Ans: (a) i = 240 mA; (b) 3.8 V
Multiloop circuits
Kirchhoff rules
Junction rule: The sum of the currents entering any junction in a
circuit must equal to the sum of currents leaving that junction.
Loop rule: The sum of the potential differences across all elements
around any closed loop must be zero.
Resistance in parallel
Sample problem 2
The elements in the circuit have
the following values: E = 12 V, R1
= 20 , R2 = 20 , R3 = 30 , R4
= 8.0  . (a) What is the current
through the battery? (b) What is
the current through R2? (c) What
is the current through R3?
Ans: (a) 0.30 A; (b) 0.18 A; (c) 0.12 A.
Sample problem 3
The elements in the circuit have
the following values: E1 = 3.0 V,
E2 = 6.0 V, R1 = 2.0 , R2 = 4.0 .
The three batteries are ideal
batteries. Find the magnitude and
direction of the current in each of
the three batteries.
Ans: i1 = 0.50 A; i2 = -0.25 A; i3 = 0.25 A.
Sample problem 4
Electric fish are able to generate current
with biological cells called electroplaques,
which are physiological emf devices. The
electroplaques in the South American eel
shown in the photograph are arranged in
140 rows, each row stretching horizontally
along the body and each containing 5000
electroplaques shown in following page.
Each electroplaque has an emf E = 0.15 V
and an internal resistance r = 0.25 . The
water surrounding the eel completes a
circuit between the two ends of
electroplaque arrays, one end at the
animal’s head and the other near its tail.
Sample problem 4 continue
(a) If the water surrounding the eel has resistance Rw = 800 , how much
current can the eel produce in the water? (b) How much current travels
through each row of the eletroplaques?
Galvanometer
Ammeter
Voltmeter
The ammeter and the voltmeter
An ideal ammeter has zero
resistance, and an ideal voltmeter
has an infinite resistance.
RC circuits
Discharging a capacitor
The RC time constant
dq
i
dt
dq q
R
 0
dt C
q  Qe
 t / RC
dq
Q  t / RC
i

e
dt
RC
i
Charging a capacitor
Charging a capacitor
dq q
R  E
dt C
q  CE(1  et / RC )
Charging a capacitor
q  CE(1  e
 t / RC
)
dq E  t / RC
i
 e
dt R
Sample problem 5
A capacitor of capacitance C is discharging through a resistor of
resistance R. (a) In terms of the time constant  = RC, when will the
charge on the capacitor be half its initial value? (b) When will the
energy stored in the capacitor be half its initial value?
Ans: (a) RCln2 = 0.69; (b) ½RCln2 = 0.35
Sample problem 6
Sample problem 7
Sample problem 8
Sample
problem 9
Sample problem 10
Sample problem 11
Infinite resistor network
Home work
Question (問題): 16, 19, 21
Exercise (練習題): 17, 20
Problem (習題): 18, 38, 42, 43, 44