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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Current Electricity Formulae Page 1

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1. Relationship between current, charge and time:

 

I =  

Q

t

 

where 

I = Current (Ampere)
Q = Charge (Coulomb)
t = time (Second)

 

(Current is defined as rate of flow of charge \ I =  

dq

dt

 )

 

2. Ohm's law:

 

V

 = R

 

(Ohm's law)

I

 

where 

V = Potential difference across a conductor.
I = Current flowing through a conductor.
R = Resistance of the conductor.

R is in ohms when V is in volts and I is in amperes.

 1 ohm =   

1 volt

 i.e. 1 W =  

1 V

1 ampere

1 A

 

3. Specific resistance:

 

3. r =   

RA

L

 

where  

r = Specific resistance or resistivity (ohm-m)

 

R = resistance of a conductor (ohm)

 

A = area of cross-section of a conductor (sq-metre)

 

l = length of a conductor (metre)

 

4. Conductance:

 

G =  

1

 = 

I

R

V

G is in Siemens or mho when R is in ohms
OR
G is in Siemens when I is in amperes and V is in volts.

 

5. Conductivity:

 

s =

1

 = 

L

r

RA

s is in siemens/metre when r is in ohm-metres.
OR
s is in siemens/metre
when,
L is in metres,
R is in ohms and A is in metre2.

 

6. Kirchhoff's 1st law:

The sum of all currents at a node is zero. i.e. S In = 0
Sign convention :

Currents entering a node 

+ sign

Currents leaving a node

- sign

Example:

 

At node A,
I1 + I2
- I3 - I4 - I5 = 0

 

7. Kirchhoff's 2nd law:

The algebraic sum of the potential. difference and e.m.f. around any closed loop in an electrical circuit is zero.
Sign convention

SInRn + SEn = 0

Across Resistance

In the direction of current

- sign

Opposite to the direction of current

+ sign

For a cell

From negative terminal to positive terminal

+ sign

From positive terminal to negative terminal

- sign

 

8. Wheatstone's Network:

 

The balancing condition for Wheatstone's bridge

P

 = 

R

Q

S


In this condition Ig = 0 and the points B and D are equipotential.

 

9. Meter Bridge:

 

(1) 

R1

 = 

l1

 

when ig = 0 (i.e. when bridge is balanced)

R2

l2

(2) l1 + l2 = 1 metre = 100 cm.

where  

l1 = length of meter bridge wire from end A (left end) to null-point.
l2 = length of meter bridge wire from end B (right end) to null-point.
R1 = resistance in left gap (unknown resistance)
R2 = resistance in right gap.

 

10. Kelvin's Method:

 

When balance point (D) is obtained,

 

R

 = 

lR

G

lg

 

\ G = R  

lg

lR

 

where  

G = resistance of the galvanometer
R = known resistance
lg = length of meter bridge wire from balance point to one end of the bridge. (opposite to galvanometer).
lR = length of meter bridge wire from balance point to other end of the bridge (length opposite to R).

 

11. Potentiometer:

 

(1)

VAP = f l1
(Principle of Potentiometer)

(2)

Potential Gradient =  

VAB

L

Where,
VAB = potential difference between points A and B.
L = total length of potentiometer wire.

(3)

E1 = VAP when galvanometer shows zero deflection.

(4)

E1 =

(

VAB

)

  l

L

Where E1 = e.m.f. of cell connected in the secondary circuit.

(

VAB

)

 = potential gradient

L

l = balancing length measured from point A to point P.

(5)

VAB = IR

 

VAB =

E

  R

Rtotal

Rtotal = R + Rc + r0
R = resistance of the wire
r0 = internal resistance of a cell of EMF(E)
Rc = control resistance connected in series with Potentiometer wire (in place of Rheostat)

(6)

Potentiometer : (Internal resistance of a cell)

 

r = R

(

l1 - l2

)

l2

 

Where  

r = internal resistance of the cell
l2 = balancing length when resistance R is connected across the cell
l1 = initial balancing length (When R =
or key in series with R is open)
R = resistance across the cell when l2 is measured.

(7)

E1

 = 

l1

 (Substituting Method)

E2

l2

 

E1,

E2 = e.m.f.s of the two cells which are being compared.
l1 = balancing length corresponding to E1
l2 = balancing length corresponding to E2.

(8)

E1

 = 

l3 + l4

 (Sum and diffrence method)

E2

l3 - l4

E1, E2 = e.m.f.s of the two cells which are being compared. (E1 > E2)
l3 = balancing length corresponding to e.m.f. (E1 + E2) i.e. cells are assisting.
l4 = balancing length corresponding to e.m.f. (E1
- E2) i.e. cells are opposing.

 

 

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