Srivastava’s Srivastava’s

Study Package

CURRENT ELECTRICITY 1. Electrical conduction a) Current instantaneous

dtdq

i

average

tq

i

it is scalar b) Current density

AJ ˆˆAi

c) Drift velocity

mleV

neAi

v d

mean free path dv d) Ohm's law (in vector form) EJ

,

e) resistance, resistivity and conductivity

AA

lAne

mlR

1

2

f) temperature coefficient of resistance

dR

dRR

RRR 10 g) temperature coefficient of resistivity

d

d

10

h) Relation between and R

R

i) equivalent temperature coefficient series RR eqeq

parallel

RReq

eq

j) Mobility of charge carrier

Evd

k) effect of temperature on conductivity

73

MARATHON-10

Current Electricity & Electrical Conduction

for conductor

for semiconductor

2. Resistance combination a) Series (current remains same in all elements) RReq

b) Parallel (potential difference is same across all elements)

RReq

11

c) Delta to star conversion : Multiply the neighbors and divide it with the sum of delta.

A

C

RA RB

B

Rc RCA RBC

RAB B A

C

CAABA

RRR where CABCAB RRR

d) Wheatstone bridge :

b

Q P

a

W

S R

if S

RQ

P then bridge is balanced and then Va = Vb. In this situation

SRQPSRQP

Req

e) Cube solution :

B

C

A

D

i) rABReq 43

(across the face diagonal)

SCO 18, 2 Floor, Sec. 20 D, CHANDIGARH. nd

Ph : 0172-6543210

Srivastava’s Srivastava’s

74

MARATHON-10 Current Electricity & Electrical Conduction

ii) rACReq 65

(across the body diagonal)

iii) rADReq 127

(across the edge)

f) Symmetry consideration i) If line of symmetry is line joining terminals corresponding points in

both halves are equipotential hence fold one half over the other. ii) If line of symmetry is perpendicular to line joining terminals all the

points on the line of symmetry are equipotential. 3. Cell and cell combination a) Cell

deal cell Real cell

r E

i) iRirEV

ii) rRV

VE

b) Cells in series and EEeq rreq

for identical cells

Rnr

nEi

if r << R then connecting cells in series is not advisable. c) Cells in parallel

r

rE

Eeq 1 and rreq

11

for identical cells

nRr

nE

Rnr

Ei

if r >> R then connecting cells in parallel is not advisable. d) Mixed combination of identical cells (battery) with m rows in parallel, each

containing n cells in series.

and nEEeq mnr

req

nrmR

NEi

where N = mn

i is maximum if and mRnr

r

mEi

2max

4. Effects of current a) Thermal effect

i) R

VRiViP

22

ii) time taken by two coils to produce same amount of heat in series

SCO 18, 2 Floor, Sec. 20 D, CHANDIGARH. Srivastava’s Srivastava’s

21 ttts

nd

Ph : 0172-6543210

75

MARATHON-10

Current Electricity & Electrical Conduction

in parallel

SCO 18, 2 Floor, Sec. 20 D, CHANDIGARH. Srivastava’s Srivastava’s

21

21ttt p

tt external resistance if internal

iii) A battery produces maximum power inresistance of battery is same as external resistance

r

EP

2

4max

ire ow melting point & low resistance wire melts if current

iv) Fuse w : L goes beyond its rated limit. Its current rating

23

ri , 2Ti b) Chemical effect

i) Farad's 1st law : qm zqm ii) Farad's 2nd law :

qEm

zE

F iii) = 96500 C = Ne (one mole of charge)

. Thermoelectricity 5 a) Seebeck effect i) Thermo emf

221TE T

Tn

Ti Thot Tc

ii) Thermoelectric power

TdE

S dT

iii) 2

cin

TTT

b) Peltier effect peltier coefficient

dqdH

J C1

c) Thomson effect thomson's coefficient

dqdH1

T

n's coefficient for led (Pb) is zero

thomso d) Relation between thermoelectric coefficients

TS

nd

Ph : 0172-6543210

MARATHON-10

76

Current Electricity & Electrical Conduction

SCO 18, 2nd Floor, Sec. 20 D, CHANDIGARH.

Ph : 0172-6543210

Srivastava’s

Srivastava’s

dS T

ircuits : a) At a junction (node) in a circuit, the incoming current equals the outgoing

the algebraic sum of the currents entering any

b) c) the effects of individual cells is same as the

oa)

dT

6. Solutions of simple c

current. In other words,junction point in a circuit is zero. The algebraic sum of the changes in potential around any closed path is zero. In an electrical circuit the sum of effect when all of them present simultaneously.

7. Gr wth and decay of current in RC circuit (transient behavior) Charging circuit

A

E

K

R C

i

i) time constant of circuit RC .

ii) RCet

RE

i

iii) c eEV

RCt

1

iv)

qq

RCt

e1max

v) 2

2 121

RCt

eCEU

vi)

RC

tRCt

eeRE

P22

vii) P is maximum at and ln2t RC2

max 4V

PR

8. b) Discharging circuit

A

K

R C

+

i

i) 0t

RCV

i eR

ii) 0

tRC

cV V e

iv) 0

tRCq CV e

v) 2

20

12

tRCU CV e