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)

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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