current electricity formula sheet
TRANSCRIPT
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)
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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
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21 ttts
nd
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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
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MARATHON-10
76
Current Electricity & Electrical Conduction
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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)
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