Current electricity formula sheet

Study Package

Srivastava’s CURRENT ELECTRICITY 1.

Electrical conduction a) Current instantaneous

i

dq dt

average

i   b)

q t

it is scalar Current density

ˆ  i A ˆ J A c)

Drift velocity vd 

i eV  neA ml

mean free path

  v d

d) e)

f)

g)

Ohm's law (in vector form)   J  E , resistance, resistivity and conductivity ml l 1   R  2 ne A A A temperature coefficient of resistance dR R  R d  R  R 0 1   R  temperature coefficient of resistivity d   d

   0 1     Relation between   and  R    R   

h) i)

equivalent temperature coefficient series Req  eq   R parallel

 eq Req j)

k)



 R

Mobility of charge carrier v  d E effect of temperature on conductivity

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Current Electricity & Electrical Conduction

 for conductor for semiconductor



2.

Resistance combination a) Series (current remains same in all elements) Req   R b)

Parallel (potential difference is same across all elements) 1 1  R eq R

c)

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

Rc



RBC

RCA

RA A

B

RAB

RB

A

B

R AB RCA where   R AB  R BC  RCA  Wheatstone bridge : a RA 

d)

P

Q W

R

S b

if P

Q

R

S

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

e)

P  Q R  S  P Q  R S

Cube solution :

C D B A i)

Req AB  

Srivastava’s

3 r 4

(across the face diagonal)

SCO 18, 2nd Floor, Sec. 20 D, CHANDIGARH. Ph : 0172-6543210

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5 r (across the body diagonal) 6 7 iii) Req AD   r (across the edge) 12 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. ii)

f)

3.

Req AC  

Cell and cell combination a) Cell E

r

Real cell

deal cell

V  E  ir  iR  E V  ii)  R  r  V  Cells in series E eq   E and req   r

i)

b)

for identical cells nE nr  R if r > R then connecting cells in parallel is not advisable. Mixed combination of identical cells (battery) with m rows in parallel, each containing n cells in series. nr E eq   nE and req   m NE i where N = mn mR  nr i is maximum if nr  mR and mE i max  2r i

c)

d)

4.

Effects of current a) Thermal effect i) ii)

V2 R time taken by two coils to produce same amount of heat in series t s  t1  t 2 P  Vi  i 2R 

Srivastava’s

SCO 18, 2nd Floor, Sec. 20 D, CHANDIGARH. Ph : 0172-6543210

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Current Electricity & Electrical Conduction

in parallel t1t 2 t1  t 2 A battery produces maximum power in external resistance if internal resistance of battery is same as external resistance E2 Pmax  4r Fuse wire : Low melting point & low resistance wire melts if current goes beyond its rated limit. Its current rating tp 

iii)

iv)

3

i  r 2, i T2

b)

Chemical effect i) Farad's 1st law : m  q  m  zq ii) Farad's 2nd law : m Eq iii)

5.

F 

E = 96500 C = Ne (one mole of charge) z

Thermoelectricity Seebeck effect a) i) Thermo emf

E   T   1  T  2

2

Tn

Ti Tc

Thot

ii)

b)

c)

d)

Thermoelectric power dE S      T  dT T  Tc iii) Tn  i 2 Peltier effect peltier coefficient dH   J C1 dq Thomson effect thomson's coefficient 1 dH   T dq thomson's coefficient for led (Pb) is zero Relation between thermoelectric coefficients   TS

Srivastava’s

SCO 18, 2nd Floor, Sec. 20 D, CHANDIGARH. Ph : 0172-6543210

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Current Electricity & Electrical Conduction

  T

dS dT

6.

Solutions of simple circuits : a) At a junction (node) in a circuit, the incoming current equals the outgoing current. In other words, the algebraic sum of the currents entering any junction point in a circuit is zero. b) The algebraic sum of the changes in potential around any closed path is zero. c) In an electrical circuit the sum of the effects of individual cells is same as the effect when all of them present simultaneously.

7.

Growth and decay of current in RC circuit (transient behavior) a) Charging circuit C R A

i

K

E time constant of circuit   RC . E t ii) i  e RC R t    iii) Vc  E 1  e RC    t    iv) q  q max 1  e RC   

i)

t    v) U  1 CE 2 1  e RC  2   t 2t 2    E  RC  e vi) P   e RC  R  

2

vii) P is maximum at t  RC ln 2 and Pmax  8.

b) Discharging circuit

C + 

V2 4R

R A

i i)

i

V0 e R

K

t  RC

ii) Vc  V0e



iv) q  CV0e

t RC 

t RC 2t

 v) U  1 CV0 2e RC 2

Srivastava’s

SCO 18, 2nd Floor, Sec. 20 D, CHANDIGARH. Ph : 0172-6543210