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 high-potential terminal (+).

dW

dqE

An ideal emf device versus a real emf device

Resistance in series

1 2 1 2( )V IR IR I R R

PowerPower of the emf device is:

emfP i E

Power transferred out is:

( ) emf rP I Ir P P E

Ir R

E

2rP I r

2( )

rP

r R r R

2 2E E

Sample problem 1The emfs and resistances in the circuit have the following values: 1 = 4.4 V, 2 = 2.1 V, r1 = 2.3 , r

2 = 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 rulesJunction 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 2The elements in the circuit have the following values: = 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: 1 = 3.0 V, 2 = 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 4Electric 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 = 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

0dq q

Rdt C

dqi

dt

/t RCq Qe

/t RCdq Qi edt RC

i

Charging a capacitor

Charging a capacitor

dq qRdt C

E

/(1 )t RCq C e E

Charging a capacitor/(1 )t RCq C e E /t RCdq

i edt R

E

Sample problem 5A 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) RCln2 = 0.69; (b) ½RCln2 = 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